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Research Interests: Mathematics, Applied Mathematics, Mathematical Physics, Pure Mathematics, Applied Mathematics and Computational Science, and 7 moreFixed Point Theorem, Numerical Analysis and Computational Mathematics, Common Fixed Point, Complete Metric Space, Electrical And Electronic Engineering, fixed point, and metric space
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In this paper we propose a solution to the nonlinear Fredholm integral equations in the context of w-distance. For this purpose, we also provide a fixed point result in the same setting. In addition, we provide best proximity point... more
In this paper we propose a solution to the nonlinear Fredholm integral equations in the context of w-distance. For this purpose, we also provide a fixed point result in the same setting. In addition, we provide best proximity point results. We give examples and present numerical results to approximate fixed points.
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1 Department of Mathematics, Faculty of natural sciences and mathematics, University of Prǐstina, Kosovska Mitrovica, Serbia, milena.petrovic@pr.ac.rs, natasa.kontrec@pr.ac.rs, stefanpnc@yahoo.com Serbian Academy of Sciences and Arts,... more
1 Department of Mathematics, Faculty of natural sciences and mathematics, University of Prǐstina, Kosovska Mitrovica, Serbia, milena.petrovic@pr.ac.rs, natasa.kontrec@pr.ac.rs, stefanpnc@yahoo.com Serbian Academy of Sciences and Arts, Belgrade, Serbia & University of Nǐs, Faculty of Sciences and Mathematics, Nǐs Serbia, vrakoc@sbb.com Politehnika, School for new technologies, Belgrade, Serbia, mladenovicjulija@gmail.com
We introduce a hybrid gradient model for solving unconstrained optimization problems based on one specific accelerated gradient iteration. Having applied a three term hybridization relation on transformed accelerated double step size... more
We introduce a hybrid gradient model for solving unconstrained optimization problems based on one specific accelerated gradient iteration. Having applied a three term hybridization relation on transformed accelerated double step size model, we develop an efficient hybrid accelerated scheme. We determine an iterative step size variable using Backtracking line search technique in which we take an optimally calculated starting value for the posed method. In convergence analysis, we show that the proposed method is at least linearly convergent on the sets of uniformly convex functions and strictly convex quadratic functions. Numerical computations confirm a significant improvement compared with some relevant hybrid and accelerated gradient processes. More precisely, subject to the number of iterations, the CPU time metric and the number of evaluations of the objective function, defined process outperforms comparative schemes multiple times.
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Using the setting of cone metric space, a fixed point theorem is proved for two maps, and several corollaries are obtained. In these cases, the cone does not need to be normal. These results generalize several well known compatible recent... more
Using the setting of cone metric space, a fixed point theorem is proved for two maps, and several corollaries are obtained. In these cases, the cone does not need to be normal. These results generalize several well known compatible recent and classical results in the literature. As an application, the existence of solution of an integral equation is presented.
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First, we define the notion of distance between two subsets in regular cone metric spaces. Then, we establish some conditions which guarantee the existence of best proximity points for cyclic contraction mappings on regular cone metric... more
First, we define the notion of distance between two subsets in regular cone metric spaces. Then, we establish some conditions which guarantee the existence of best proximity points for cyclic contraction mappings on regular cone metric spaces.
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ABSTRACT Ilić and Rakočević [6] proved a fixed point theorem for quasi-contractive mappings on cone metric spaces when the underlying cone is normal. Recently, Z. Kadelburg, S. Radenović, and V. Rakočević obtained a similar result without... more
ABSTRACT Ilić and Rakočević [6] proved a fixed point theorem for quasi-contractive mappings on cone metric spaces when the underlying cone is normal. Recently, Z. Kadelburg, S. Radenović, and V. Rakočević obtained a similar result without using the normality condition but only for a contractive constant λ ∈ (0, 1/2) [8]. In this note, using a new method of proof, we prove this theorem for any contractive constant λ ∈ (0, 1).
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We consider quasicontraction nonself-mappings on Takahashi convex metric spaces and common fixed point theorems for a pair of maps. Results generalizing and unifying fixed point theorems of Ivanov, Jungck, Das and Naik, and Ćirić are... more
We consider quasicontraction nonself-mappings on Takahashi convex metric spaces and common fixed point theorems for a pair of maps. Results generalizing and unifying fixed point theorems of Ivanov, Jungck, Das and Naik, and Ćirić are established.
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Using the setting of cone metric space, a fixed point theorem is proved for two maps, and several corollaries are obtained. In these cases, the cone does not need to be normal. These results generalize several well known compatible recent... more
Using the setting of cone metric space, a fixed point theorem is proved for two maps, and several corollaries are obtained. In these cases, the cone does not need to be normal. These results generalize several well known compatible recent and classical results in the literature. As an application, the existence of solution of an integral equation is presented.
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We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between... more
We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between certain sequence spaces, in solving infinite systems of integral equations in some sequence spaces. We also present some recent results related to the existence of best proximity points (pairs) for some classes of cyclic and noncyclic condensing operators in Banach spaces equipped with a suitable measure of noncompactness. Finally, we discuss the existence of an optimal solution for systems of integro–differentials.
Research Interests: Mathematics and Axioms
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In this paper, we extend the notion of) , ( G-contraction, introduced by Ozturk and Girgin, to multi-valued mappings. By using our new notion we prove a fixed point theorem for multi-valued mappings. Our results imply Nadler's... more
In this paper, we extend the notion of) , ( G-contraction, introduced by Ozturk and Girgin, to multi-valued mappings. By using our new notion we prove a fixed point theorem for multi-valued mappings. Our results imply Nadler's theorem, and generalized version of Nadler's theorem on partial metric spaces.
In 1968, M. G. Maia [16] generalized Banach’s fixed point theorem for a set X endowed with two metrics. In 2014, Ansari [2]introduced the concept of C-class functions and generalized many fixed point theorems in the literature. In this... more
In 1968, M. G. Maia [16] generalized Banach’s fixed point theorem for a set X endowed with two metrics. In 2014, Ansari [2]introduced the concept of C-class functions and generalized many fixed point theorems in the literature. In this paper, we prove some Maia’s type fixed point results via C-class function in the setting of two metrics space endowed with a binary relation. Our results, generalized and extended many existing fixed point theorems, for generalized contractive and quasi-contractive mappings, in a metric space endowed with binary relation.
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In this manuscript, we define a new contraction mapping, Pata-Ćirić type contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ćirić. We proved that in a complete space, each Pata-Ćirić type contraction at... more
In this manuscript, we define a new contraction mapping, Pata-Ćirić type contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ćirić. We proved that in a complete space, each Pata-Ćirić type contraction at a point possesses a fixed point. We express an example to illustrate the observed result.
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In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi bmetric spaces is obtained. Some examples... more
In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi bmetric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (?-?)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.
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Research Interests: Mathematics and Operator
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Some common fixed point theorems for a pair of nonself-mappings in complete metrically convex metric spaces are proved by alte ring distances between the points, which generalize earlier results due to M. D. Khan and Bharadwaj (2001), M.... more
Some common fixed point theorems for a pair of nonself-mappings in complete metrically convex metric spaces are proved by alte ring distances between the points, which generalize earlier results due to M. D. Khan and Bharadwaj (2001), M. S. Khan et al. (2000), Bianchini (1972), Chatterjea 1972, and others. Some related results are also discussed besides furnishing an illustrative example.