The purpose of this paper is to introduce and investigate ?-monotone operators and ?-monotone bifunctions in the context of Banach space. Local boundedness of ?-monotone bifunctions in the interior of their domains is proved. Also, the... more
The purpose of this paper is to introduce and investigate ?-monotone operators and ?-monotone bifunctions in the context of Banach space. Local boundedness of ?-monotone bifunctions in the interior of their domains is proved. Also, the difference of two ?-monotone operators is studied. Moreover, some relations between ?-monotonicity and ?-convexity are investigated.
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Abstract. Suppose 51(E, F) is the space of all absolutely 1-summing operators between two Banach spaces E and F. We show that if F has a copy of c0, then 51(E, F) will have a copy of c0, and under some conditions if E has a copy of `1... more
Abstract. Suppose 51(E, F) is the space of all absolutely 1-summing operators between two Banach spaces E and F. We show that if F has a copy of c0, then 51(E, F) will have a copy of c0, and under some conditions if E has a copy of `1 then 51(E, F) would have a complemented copy of `1.
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In this paper, we study the existence of three solutions to the p(x)-Kirchhoff type equations in R^N. By means of nonsmooth three critical points theorem and the theory of the variable exponent Sobolev spaces, we establish the existence... more
In this paper, we study the existence of three solutions to the p(x)-Kirchhoff type equations in R^N. By means of nonsmooth three critical points theorem and the theory of the variable exponent Sobolev spaces, we establish the existence of three critical points for the problem. Moreover, we study the existence of three radially symmetric solutions for a class of quasilinear elliptic inclusion problem with discontinuous nonlinearities in R^N. Our approach is based on critical point theory for locally Lipschitz functionals due to Iannizzotto.
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The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of ... more
The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to a nonlinear heat equation illustrating the application of the theory.
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The aim of this paper is to establish some uniqueness and well-posedness results for a general inequality of equilibrium problems type involving \alpha-monotone bifunction, whose solution is sought in a subset K of a Banach space X. By... more
The aim of this paper is to establish some uniqueness and well-posedness results for a general inequality of equilibrium problems type involving \alpha-monotone bifunction, whose solution is sought in a subset K of a Banach space X. By introducing several concepts of well-posedness for generalized equilibrium problems considered, we establish some metric characterizations of well posedness. Moreover, we prove that the well-posedness of generalized equilibrium problems is equivalent to the existence and uniqueness of its solution.
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In this article, we study the variational-hemivariational inequalities with Neumann boundary condition. Using a nonsmooth critical point theorem, we prove the existence of infinitely many solutions for boundaryvalue problems. Our... more
In this article, we study the variational-hemivariational inequalities with Neumann boundary condition. Using a nonsmooth critical point theorem, we prove the existence of infinitely many solutions for boundaryvalue problems. Our technical approach is based on variational methods.
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This paper describes the moderateness of Short-time Fourier Transform by the Caputo Fractional Derivative. Moreover, we consider some properties of the generalized STFT in extended Colmbeau Algebra.
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A new class of nonlinear set-valued variationalinclusions involving $(A,eta)$-monotone mappings in a Banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(A,eta)$-monotonicity,... more
A new class of nonlinear set-valued variationalinclusions involving $(A,eta)$-monotone mappings in a Banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(A,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.
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In this paper, we consider the existence result of a nonstandard hemivariational inequalities with -monotone mapping in reflexive and non reflexive Banachs space. Finally, we provide sufficient conditions for which that inequality has a... more
In this paper, we consider the existence result of a nonstandard hemivariational inequalities with -monotone mapping in reflexive and non reflexive Banachs space. Finally, we provide sufficient conditions for which that inequality has a solution in the case of unbounded sets, via the fixed point and KKM theorems.
Research Interests: Mathematics, Pure Mathematics, Inequality, Fixed Point Theorem, H, and 3 moreE, J, and Existence of solutions
This paper deals with a new type of xed point, i.e; "xed point of order 2" which is introduced in a metric space and some results are achieved.
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This paper deals with fixed point theory and fixed point property in minimal spaces. We will prove that under some conditions f : (X,M) → (X,M) has a fixed point if and only if for each m-open cover {Bα} for X there is at least one x ∈ X... more
This paper deals with fixed point theory and fixed point property in minimal spaces. We will prove that under some conditions f : (X,M) → (X,M) has a fixed point if and only if for each m-open cover {Bα} for X there is at least one x ∈ X such that both x and f(x) belong to a common Bα. Further, it is shown that if (X,M) has the fixed point property, then its minimal retract subset enjoys this property.
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In this paper hemivariational inequality with nonhomogeneous Neumann boundary condition is investigated. The existence of infinitely many small solutions involving a class of p(x) - Laplacian equation in a smooth bounded domain is... more
In this paper hemivariational inequality with nonhomogeneous Neumann boundary condition is investigated. The existence of infinitely many small solutions involving a class of p(x) - Laplacian equation in a smooth bounded domain is established. Our main tool is based on a version of the symmetric mountain pass lemma due to Kajikiya and the principle of symmetric criticality for a locally Lipschitz functional.
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In this article, we use the edge-type of Sobolev inequality,Hardy inequlity and Poincaré inequality to prove the existence theorem for a class of semilinear degenerate hypoelliptic equation on manifolds with conical singularities. In this... more
In this article, we use the edge-type of Sobolev inequality,Hardy inequlity and Poincaré inequality to prove the existence theorem for a class of semilinear degenerate hypoelliptic equation on manifolds with conical singularities. In this paper we shall find the existence theorem for the problem 1.1 in cone Sobolev space $${\mathcal {H}}^{1,\frac{N}{2}}_{2,0}({\mathbb {E}}).$$H2,01,N2(E). Finally, we obtain existence result of global solutions with exponential decay and show the blow-up in finite time of solutions.
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In this paper some asymptotic behaviors of the Pexiderized additive mappings can be proved for functions on commutative semigroup to a complex normed linear space under some suitable conditions. As a consequence of our result, we give... more
In this paper some asymptotic behaviors of the Pexiderized additive mappings can be proved for functions on commutative semigroup to a complex normed linear space under some suitable conditions. As a consequence of our result, we give some generalizations of Skof theorem and S. M. Joung theorem. Furthermore, in this note we present a armative answer to problem 18, in the thirty-rst ISFE.
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ABSTRACT
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A new class of nonlinear set-valued variational inclusions involving (A,η)-monotone mappings in a Banach space setting is introduced and then, based on the generalized resolvent operator technique associated with (A,η)-monotonicity, the... more
A new class of nonlinear set-valued variational inclusions involving (A,η)-monotone mappings in a Banach space setting is introduced and then, based on the generalized resolvent operator technique associated with (A,η)-monotonicity, the existence and approximate solvability is investigated using an iterative algorithm and fixed point theory.
In this paper we propose a new version of cooperative games. In fact, the notion of cooperative games and their concavifications are extended. As a consequence, in this new setting it turns out that coreV≠∅ if and only if cav(u)(C Ω )=u(C... more
In this paper we propose a new version of cooperative games. In fact, the notion of cooperative games and their concavifications are extended. As a consequence, in this new setting it turns out that coreV≠∅ if and only if cav(u)(C Ω )=u(C Ω ).
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This paper deals with hyper metric spaces as a generalization of metric spaces. Hyper convergent sequence, hyper continuous function and hyper contraction map are introduced and some results in these settings are investigated. In... more
This paper deals with hyper metric spaces as a generalization of metric spaces. Hyper convergent sequence, hyper continuous function and hyper contraction map are introduced and some results in these settings are investigated. In particular, it is found that any hyper contraction map on a hyper metric space (X,D) has a unique fixed point. Finally, Cantor’s theorem and the Baire category theorem in hyper metric space are given.
The notion of hyper (quasi, semi) norm is introduced, which is an extended version of (quasi, semi) norm. Moreover, some basic properties of hyper (quasi, semi) normed spaces that are compatible in the classical case are investigated.... more
The notion of hyper (quasi, semi) norm is introduced, which is an extended version of (quasi, semi) norm. Moreover, some basic properties of hyper (quasi, semi) normed spaces that are compatible in the classical case are investigated. Some characterizations of convergent sequences, continuous and bounded functions via hyper (quasi, semi) normed spaces are considered. It is shown that a hyper (quasi, semi) normed space is hyper complete if and only if it is hyper sequentially complete.
This note deals with fixed point theorems via p-star shaped subsets of topological vector spaces. By using Fan-KKM principle in generalized convex space, a fixed point theorem due to Park is achieved for a compact mapping on a p-star... more
This note deals with fixed point theorems via p-star shaped subsets of topological vector spaces. By using Fan-KKM principle in generalized convex space, a fixed point theorem due to Park is achieved for a compact mapping on a p-star shaped subset of a topological vector space. Moreover, some fixed point theorems for non-expansive self-mapping on p-star shaped sets are considered. It is shown that every non-expansive self-mapping of compact p-star shaped subset of a Banach space has a fixed point in K.
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ABSTRACT In this note, we present some results on maximality of the difference of two monotone operators. It is shown that, for two multifunctions S and T from X to X *, maximal monotonicity of S and monotonicity of both T and S−T imply... more
ABSTRACT In this note, we present some results on maximality of the difference of two monotone operators. It is shown that, for two multifunctions S and T from X to X *, maximal monotonicity of S and monotonicity of both T and S−T imply maximal monotonicity of S−T.
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This paper deals with existence and uniqueness of the solution for a system of variational inclusions with (A, ? )-monotone mappings.
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ABSTRACT The purpose of this paper is devoted to generalize the concept of fuzzy compactness. In fact we have introduce the concept of fuzzy (countably) compactness in fuzzy minimal spaces and some related basic results in these new... more
ABSTRACT The purpose of this paper is devoted to generalize the concept of fuzzy compactness. In fact we have introduce the concept of fuzzy (countably) compactness in fuzzy minimal spaces and some related basic results in these new setting are given. Further, some results of fuzzy compactness for fuzzy topological spaces are achieved. For example, it is shown that (X,M) is fuzzy m-compact if and only if every fuzzy m-open cover of it has a finite 0-partition. Furthermore, every fuzzy m − CII space is a fuzzy m-Lindelof space.
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This paper deals with minimal linear spaces, m-continuity and m-boundedness. In particular, it is found that in a linear minimal space (X,M) the assignment x↦t0x+x0 from X to X is m-continuous. On the other hand, the convex hull of an... more
This paper deals with minimal linear spaces, m-continuity and m-boundedness. In particular, it is found that in a linear minimal space (X,M) the assignment x↦t0x+x0 from X to X is m-continuous. On the other hand, the convex hull of an m-neighborhood of 0 is an m-neighborhood if (X,M) has property U.
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ABSTRACT This paper deals with the concepts of fuzzy minimal separation and fuzzy closed minimal separation. Some criterion for m-separatedness and Cm-separatedness of two fuzzy sets in a fuzzy minimal space are achieved. Further, it is... more
ABSTRACT This paper deals with the concepts of fuzzy minimal separation and fuzzy closed minimal separation. Some criterion for m-separatedness and Cm-separatedness of two fuzzy sets in a fuzzy minimal space are achieved. Further, it is shown that for any fuzzy sets C and D in Y, A × C and B × D are fuzzy m-separated (Cm-separated) in X × Y, if A and B are fuzzy m-separated (Cm-separated) sets in X. Moreover, c.A and c.B are fuzzy m-separated (Cm-separated) if and only if A and B are fuzzy m-separated (Cm-separated).