Reza Arab
Islamic Azad University Sari Branch, Department of Mathematics, Department Member
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The purpose of this paper is to establish some fixed point theorems for a mapping having a monotone property satisfying a contractive condition of rational type in the partially ordered b-metric spaces. The results presented in the paper... more
The purpose of this paper is to establish some fixed point theorems for a mapping having a monotone property satisfying a contractive condition of rational type in the partially ordered b-metric spaces. The results presented in the paper generalize and extend several well-known results in the literature. An example is given to support the usability of our results.
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In this paper, we prove common fixed point results of sequence of self mappings in b-metric spaces. The results presented in this paper generalize some recent results announced by many authors. We demonstrate these facts by some examples.... more
In this paper, we prove common fixed point results of sequence of self mappings in b-metric spaces. The results presented in this paper generalize some recent results announced by many authors. We demonstrate these facts by some examples. Finally, an application to existence problem for an integral equation is presented.
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In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the... more
In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tychonoff fixed point theorem. Also, we present an example of nonlinear integral equations to show the efficiency of our results. Our results extend several comparable results obtained in the previous literature.
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We prove some fixed and common fixed point theorems for two weakly compatible self mappings in complete b−metric spaces. Our results improve and generalize several known results from the current literature and its extension.
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Best proximity results for cyclic and noncyclic -contractive operators in (strictly convex) Banach spaces are obtained via the measure of noncompactness. The work extends some of recent investigations in this direction. The obtained... more
Best proximity results for cyclic and noncyclic -contractive operators in (strictly convex) Banach spaces are obtained via the measure of noncompactness. The work extends some of recent investigations in this direction. The obtained results are applied to investigation of optimum solutions for a system of second order differential equations with two initial conditions followed by an example.
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In this paper, we prove triple common fixed point theorems in partially ordered b-metric spaces depended on another function. The presented results generalize the theorem of Aydi, Karapinar and Mustafa [9], Berinde and Borcut [16], Borcut... more
In this paper, we prove triple common fixed point theorems in partially ordered b-metric spaces depended on another function. The presented results generalize the theorem of Aydi, Karapinar and Mustafa [9], Berinde and Borcut [16], Borcut and Berinde [19] and Borcut [20]. Our results extend and improve several known results from the context of ordered metric spaces to the setting of ordered b-metric spaces. As an application, we prove the existence of a unique solution to a class of nonlinear integral equations.
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In this article, we discuss about solvability of infinite systems of singular integral equations with two variables in the Banach sequence space $C(I times I, c)$ by applying measure of noncompactness and Meir-Keeler condensing... more
In this article, we discuss about solvability of infinite systems of singular integral equations with two variables in the Banach sequence space $C(I times I, c)$ by applying measure of noncompactness and Meir-Keeler condensing operators. By presenting an example, we have illustrated our results. For validity of the results we introduce a modified semi-analytic method in the case of two variables to make an iteration algorithm to find a closed-form of solution for the above problem. The numerical results show that the produced sequence for approximating the solution of example is in the $c$ space with a high accuracy.
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In the present article, we introduce a new concept of contraction and prove a new type of the extension of Tychonoff fixed point theorem. Then, as an application, we study the problem of existence of solutions for the infinite systems of... more
In the present article, we introduce a new concept of contraction and prove a new type of the extension of Tychonoff fixed point theorem. Then, as an application, we study the problem of existence of solutions for the infinite systems of integral equations using the technique of measures of noncompactness in conjunction with this extension in the Fréchet spaces. 2010 Mathematics Subject Classification: 54H25; 47H10
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We propose to investigate the solutions of system of functional-integral equations in the setting of measure of noncompactness on real-valued bounded and continuous Banach space. To achieve this, we first establish some new Darbo... more
We propose to investigate the solutions of system of functional-integral equations in the setting of measure of noncompactness on real-valued bounded and continuous Banach space. To achieve this, we first establish some new Darbo type fixed and coupled fixed point results for $mu$-set $(omega,vartheta)$-contraction operator using arbitrary measure of noncompactness in Banach spaces. An example is given in support for the solutions of a pair of system of functional-integral equations.
In this paper, we consider a new class of pairs of generalized contractive type mappings defined in G−metric spaces. Some coincidence and common fixed point results for these mapping are presented. Our results extend and generalize many... more
In this paper, we consider a new class of pairs of generalized contractive type mappings defined in G−metric spaces. Some coincidence and common fixed point results for these mapping are presented. Our results extend and generalize many known results in the literature.An example is presented to show the ectiveness of our results.
The aim of this paper is to show how some measures of noncompactness in the Banach space of continuous functions defined on two variables can be applied to the solvability of a general system of functional integral equations . The results... more
The aim of this paper is to show how some measures of noncompactness in the Banach space of continuous functions defined on two variables can be applied to the solvability of a general system of functional integral equations . The results obtained generalize and extend several equations . An illustrative example is also presented .
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In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these... more
In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these spaces. Finally, as an application, we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixed point theorem associated with these new measures of noncompactness. Further, some examples are presented to show the efficiency of our results.
The aim of the present research was to explore the relationship between emotional intelligence and conflict management styles in staffs at the Bank of Sepah, Tehran. The research methodology is descriptive and falls under correlative... more
The aim of the present research was to explore the relationship between emotional intelligence and conflict management styles in staffs at the Bank of Sepah, Tehran. The research methodology is descriptive and falls under correlative forms. The statistical population consisted of all Sepah staffs in the city of Tehran, where based on the latest statistics and information, the number of 2000 staffs participated. Using cluster sampling method, the number of 322 people was selected as the sample. In order to measure variables used in the research, two questionnaires, i.e. Robins' Staffs Conflict Management Styles (2001) and Schering's Emotional Intelligence (1996) were applied. The validity of both questionnaires was confirmed by experts and, based on Cronbach's alpha the reliability of the scales was found to be 0/89 for the staffs conflicts and 0/86 for emotional intelligence. To analyze data, descriptive and inferential (Pearson correlation coefficient, single t test and...
In this article, solvability of infinite system of nonlinear singular integral equations of two variables in Banach sequence spaces $$c_{0}$$ c 0 and $$\ell _{1}$$ ℓ 1 is investigated. For this purpose, Hausdorff measure of noncompactness... more
In this article, solvability of infinite system of nonlinear singular integral equations of two variables in Banach sequence spaces $$c_{0}$$ c 0 and $$\ell _{1}$$ ℓ 1 is investigated. For this purpose, Hausdorff measure of noncompactness (in short, Hausdorff MNC) and Meir–Keeler condensing operators are employed. The guarantee of our results are given by some examples. Also to approach an approximation of semi-analytic solution, we introduce a coupled modified homotopy perturbation and Adomian decomposition method. Thus, an iterative algorithm is constructed to find the above solution. The numerical results show that the produced sequence to approximate the solution has a high accuracy.
In this article, we establish some generalization of Darbo type coupled fixed point theorem and give some results on the existence of solutions for a system of nonlinear functional integral equations in Banach space. We illustrated the... more
In this article, we establish some generalization of Darbo type coupled fixed point theorem and give some results on the existence of solutions for a system of nonlinear functional integral equations in Banach space. We illustrated the results with the help of an example.
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We propose two new notion of contraction mappings involving measure of noncompactness in the frame work of Banach space and derive some basic Darbo type fixed and coupled fixed point results. The results are correlated with the classical... more
We propose two new notion of contraction mappings involving measure of noncompactness in the frame work of Banach space and derive some basic Darbo type fixed and coupled fixed point results. The results are correlated with the classical Banach fixed point theorems. Further we show the applicability of obtained results to the theory of integral equations following a concrete example which illustrate the application part.
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Abstract The purpose of this article is to introduce a new tempered sequence space and obtain the measure of noncompactness in this space. Using the measure of noncompactness and generalized Darbo fixed point theorem, we discuss the... more
Abstract The purpose of this article is to introduce a new tempered sequence space and obtain the measure of noncompactness in this space. Using the measure of noncompactness and generalized Darbo fixed point theorem, we discuss the existence of solutions of an infinite system of fractional differential equations. Also we provide an example to highlight and establish the importance of our main result. Finally, we approach the solution of the example with high accuracy, by a convergent iterative algorithm with the help of modified homotopy perturbation method.
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Fractional dynamics is a scope of study in science considering the action of systems. These systems are designated by utilizing derivatives of arbitrary orders. In this effort, we discuss the sufficient conditions for the existence of the... more
Fractional dynamics is a scope of study in science considering the action of systems. These systems are designated by utilizing derivatives of arbitrary orders. In this effort, we discuss the sufficient conditions for the existence of the mild solution (m-solution) of a class of fractional dynamic systems (FDS). We deal with a new family of fractional m-solution in Rn for fractional dynamic systems. To accomplish it, we introduce first the concept of (F, ψ)-contraction based on the measure of noncompactness in some Banach spaces. Consequently, we establish requisite fixed point theorems (FPTs), which extend existing results following the Krasnoselskii FPT and coupled fixed point results as a outcomes of derived one. Finally, we give a numerical example to verify the considered FDS, and we solve it by iterative algorithm constructed by semianalytic method with high accuracy. The solution can be considered as bacterial growth system when the time interval is large.
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Primarily this work intends to prove the best proximity point (pair) results using the concept of measure of noncompactness and simulation functions. The obtained results generalize and extend some present state of the art on Darbo type... more
Primarily this work intends to prove the best proximity point (pair) results using the concept of measure of noncompactness and simulation functions. The obtained results generalize and extend some present state of the art on Darbo type fixed point theorems. The main results are applied to actualize the optimum solutions of a system of nonlinear mixed Fredholm–Volterra functional integro-differential equations with local initial conditions.
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We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive... more
We investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.
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Abstract In this article, we establish the existence of solution for two dimensional nonlinear fractional integral equation using fixed point theorem and measure of noncompactness. Applicability of our results is shown by some examples... more
Abstract In this article, we establish the existence of solution for two dimensional nonlinear fractional integral equation using fixed point theorem and measure of noncompactness. Applicability of our results is shown by some examples and for validity of the proposed method we make an iterative algorithm by semi-analytic technique that finds a closed form of the solution with an acceptable accuracy. Ability of the proposed method is granted by comparison with another method found in existing literature.
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In this paper, we create tripled fixed point outcomes via a subjective measure of noncompactness in the sense of Banas and Goebel. Furthermore, we introduce some applications of the measure of noncompactness notion to functional equations... more
In this paper, we create tripled fixed point outcomes via a subjective measure of noncompactness in the sense of Banas and Goebel. Furthermore, we introduce some applications of the measure of noncompactness notion to functional equations including nonlinear integral equations as well as local fractional integral equations.
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Abstract In this paper we prove existence of solution for infinite system of nonlinear integral equations in the Banach spaces l p , p > 1 with the help of a technique associated with measure of noncompactness and generalized... more
Abstract In this paper we prove existence of solution for infinite system of nonlinear integral equations in the Banach spaces l p , p > 1 with the help of a technique associated with measure of noncompactness and generalized Meir–Keeler fixed point theorem. We also provide some illustrative examples in support of our existence theorems. Finally, we introduce an iteration algorithm constructed by modified homotopy perturbation method to solve the above problem with high accuracy.
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The purpose of this work is to present two new notions of $$\mu $$μ-set contraction of a bounded subset of a Banach space and establish some fixed point and coupled fixed point results in the direction of Darbo (Rend Sem Math Univ Padova... more
The purpose of this work is to present two new notions of $$\mu $$μ-set contraction of a bounded subset of a Banach space and establish some fixed point and coupled fixed point results in the direction of Darbo (Rend Sem Math Univ Padova 4:84–92, 1995). We apply our work to get existence of solutions to nonlinear functional-integral equations followed by an illustration. Our work generalizes many existing results in the literature.
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Abstract The objective of this article is to establish a fixed point theorem using different class of control functions, which is a generalization of Darbo’s fixed point theorem (DFPT) and its various versions obtained by several authors.... more
Abstract The objective of this article is to establish a fixed point theorem using different class of control functions, which is a generalization of Darbo’s fixed point theorem (DFPT) and its various versions obtained by several authors. Using this result we obtain existence of at least one positive solution for a quadratic integral equation of Fredholm type.
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In this present paper, we introduce a measure of noncompactness on the space $$C^{n} [a,b]$$Cn[a,b]. As an application, we study the problem of existence of solutions of Fredholm integral–differential equations using the technique of... more
In this present paper, we introduce a measure of noncompactness on the space $$C^{n} [a,b]$$Cn[a,b]. As an application, we study the problem of existence of solutions of Fredholm integral–differential equations using the technique of measures of noncompactness in conjunction with Darbo’s fixed point theorem. Further, we give some illustrative examples to verify the effectiveness and applicability of our results.
Research Interests: Mathematics and Geology
This paper intends to reread what Richard Rorty introduced as ironist in the context of one of the most contested topics in the realm of social sciences; i.e. agency and structure. Rorty maintains that ironist is the potential citizen of... more
This paper intends to reread what Richard Rorty introduced as ironist in the context of one of the most contested topics in the realm of social sciences; i.e. agency and structure. Rorty maintains that ironist is the potential citizen of utopian liberal democracy. An ironist, in his words, is a person who a) has radical and continuing doubts about the final vocabulary she currently uses, b) realizes that argument phrased in her present vocabulary can neither underwrite nor dissolve possible doubts, and c) she does not think that her vocabulary is closer to reality than others. The main question of this study is where this conscious subject stands within the context of agency-structure dispute. First, relevant literature on the dichotomy is going to be examined, and then, while discussing other relevant terms in his philosophy, this paper will show how Rorty solves the agentic problem of his ironist with his introducing of the public-private distinction.
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Abstract The purpose of this paper is to obtain some common fixed point results for two mappings satisfying various contractive conditions in metric-like spaces. These results extend some previous results in the literature, since the... more
Abstract The purpose of this paper is to obtain some common fixed point results for two mappings satisfying various contractive conditions in metric-like spaces. These results extend some previous results in the literature, since the condition under which the operator admits common fixed points is more general than the others in literature. Therefore, several well known results are generalized. As an application we use these results to existence of solution for nonlinear quadratic integral equation. To credibility, we apply modified homotopy and Adomian decomposition method to find solution of the above problem with high accuracy.
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The aim of this paper is to introduce a new measure of noncompactness on the Sobolev space $W^{n,p}[0,T]$. As an application, we investigate the existence of solutions for some classes of functional integro-differential equations in this... more
The aim of this paper is to introduce a new measure of noncompactness on the Sobolev space $W^{n,p}[0,T]$. As an application, we investigate the existence of solutions for some classes of functional integro-differential equations in this space using Darbo’s fixed point theorem.
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In this article, the existence of a solution for a nonlinear integral equation with deviating argument that appears in nonlinear analysis and its applications is discussed. So, to do this, the technique of noncompactness measure and the... more
In this article, the existence of a solution for a nonlinear integral equation with deviating argument that appears in nonlinear analysis and its applications is discussed. So, to do this, the technique of noncompactness measure and the basic fixed point theorems such as Darbo's theorem, in Banach algebra are employed. Then, a powerful numerical approach based on Sine quadrature is presented to estimate a solution for this equation. Finally, some numerical examples are given to confirm efficiency and accuracy of the numerical scheme.
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ABSTRACT In the present paper we investigate the construction of compact sets of bounded continuous functions on unbounded set $\Omega$ of $\Bbb{R}^n$, and then introduce a measure of noncompactness on this space. As an application,... more
ABSTRACT In the present paper we investigate the construction of compact sets of bounded continuous functions on unbounded set $\Omega$ of $\Bbb{R}^n$, and then introduce a measure of noncompactness on this space. As an application, we study the existence of entire solutions for a class of nonlinear functional integral equations of Volttra type by using some fixed point theorems associated with this new measure of noncompactness. Obtained results generalize several main results. We will also include some examples which show that our results are applicable where the previous ones are not.
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ABSTRACT In the present paper, using the concept of measure of non-compactness, we introduce the concept of a new contraction on a Banach space and obtain few generalizations of Darbo’s fixed-point theorem and extend some recent results... more
ABSTRACT In the present paper, using the concept of measure of non-compactness, we introduce the concept of a new contraction on a Banach space and obtain few generalizations of Darbo’s fixed-point theorem and extend some recent results of (Aghajani et al., J. Comput. Appl. Math. 260:68–77, 2014) and (Aghajani et al., Bull. Belg. Math. Soc. Simon Stevin 20:345–358, 2013). Also we show the applicability of obtained results to the theory of integral equations. A concrete example illustrating the mentioned applicability is also included.
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We introduce the notion of almost generalized ( ψ , φ , L ) -contractive mappings, and establish the coincidence and common fixed point results for this class of mappings in partially ordered complete b-metric spaces. Our results extend... more
We introduce the notion of almost generalized ( ψ , φ , L ) -contractive mappings, and establish the coincidence and common fixed point results for this class of mappings in partially ordered complete b-metric spaces. Our results extend and improve several known results from the context of ordered metric spaces to the setting of ordered b-metric spaces. As an application, we prove the existence of a unique solution to a class of nonlinear quadratic integral equations.
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ABSTRACT The aim of this paper is to establish fixed point theorems for condensing operators in the Fréchet spaces. In our considerations we apply the technique of measures of noncompactness in conjunction with the Tychonoff fixed point... more
ABSTRACT The aim of this paper is to establish fixed point theorems for condensing operators in the Fréchet spaces. In our considerations we apply the technique of measures of noncompactness in conjunction with the Tychonoff fixed point theorem. Moreover, as an application, we study the problem of the existence of solutions for infinite systems of integral equations in two variables. The results obtained extend several ones. Finally, an example is presented to show the efficiency of our results.
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To assess the presences of Escherichia coli, its serogroups, virulence factors and antibiotic resistance properties in ruminant's meat, a total of 820 raw... more
To assess the presences of Escherichia coli, its serogroups, virulence factors and antibiotic resistance properties in ruminant's meat, a total of 820 raw meat samples were collected and then evaluated using culture, PCR and disk diffusion methods. Totally, 238 (29.02%) samples were positive for presence of Escherichia coli. All of the isolates had more than one virulence gene including Stx1, Stx2, eaeA and ehly. All investigated serogroups were found in beef and sheep and all except O145, O121 and O128 were found in goat. The O91, O113, O111, O103, O26 and O157 serogroups were found in camel. Totally, aadA1-blaSHV combination was the most predominant antibiotic resistance gene. The highest resistance of STEC strains was seen against penicillin while resistance to nitrofurantoin and ciprofloxacin was minimal. These findings showed that health care and meat inspection should be reconsidered in Iranian slaughterhouses and butchers.