e newest generalization of the Banach contraction through the notions of the generalized F-contra... more e newest generalization of the Banach contraction through the notions of the generalized F-contraction, simulation function, and admissible function is introduced. e existence and uniqueness of fixed points for a self-mapping on complete metric spaces by the new constructed contraction are investigated. e results of this article can be viewed as an improvement of the main results given in the references.
In this paper, the notion of strictly (α, η, ψ, ξ)-contractive multi-valued mappings is introduce... more In this paper, the notion of strictly (α, η, ψ, ξ)-contractive multi-valued mappings is introduced where the continuity of ξ is relaxed. The existence of fixed point theorems for such mappings in the setting of α-η-complete partial metric spaces are provided. The results of the paper can be viewed as the extension of the recent results obtained in the literature. Furthermore, we assure the fixed point theorems in partial complete metric spaces endowed with an arbitrary binary relation and with a graph using our obtained results.
We consider a new class of complementarity problems for η-pseudomonotone maps and obtain an exist... more We consider a new class of complementarity problems for η-pseudomonotone maps and obtain an existence result for their solutions in real Hausdorff topological vector spaces. Our results extend the same previous results in this literature.
Nonlinear functional analysis and applications, Apr 13, 2016
In this paper, we first give a generalization of Takahashi's existence theorem for a vector v... more In this paper, we first give a generalization of Takahashi's existence theorem for a vector valued mapping. From the existence theorem, we establish a generalized Caristi's fixed point theorem and a generalized vector Ekeland's variational principle. As an application, we show that if a differentiable function F with values in a Banach lattice has a order lower bound (although it need not attain it), then for every e> 0, there exists some point u_e, where |F(u_e)|
We introduce a new family of mappings on [0, +∞) by relaxing the nondecreasing condition on the m... more We introduce a new family of mappings on [0, +∞) by relaxing the nondecreasing condition on the mappings and by using the properties of this new family we present some fixed point theorems for-contractive-type mappings in the setting of complete metric spaces. By applying our obtained results, we also assure the fixed point theorems in partially ordered complete metric spaces and as an application of the main results we provide an existence theorem for a nonlinear differential equation.
Journal of Inequalities and Applications, May 2, 2014
Recently Huang et al. (Math. Comput. Model. 43:1267-1274, 2006) introduced a class of parametric ... more Recently Huang et al. (Math. Comput. Model. 43:1267-1274, 2006) introduced a class of parametric implicit vector equilibrium problems (for short PIVEP) and they presented some existence results for a solution of PIVEP. Also, they provided two theorems about upper and lower semi-continuity of the solution set of PIVEP in a locally convex Hausdorff topological vector space. The paper extends the corresponding results obtained in the setting of topological vector spaces with mild assumptions and removing the notion of locally non-positiveness at a point and lower semi-continuity of the parametric mapping.
We first introduce the notion of-upper sign property which is an extension of the upper sign prop... more We first introduce the notion of-upper sign property which is an extension of the upper sign property introduced in Castellani and Giuli, 2013, by relaxing convexity on the set. Afterwards, we establish a link between the solution sets of local dual equilibrium problem (Minty local equilibrium problem) and equilibrium problem for mappings whose domains are not necessarily convex by relaxing the upper sign continuity on the map, as it is assumed in the literature (Bianchi and Pini, 2005; Castellani and Giuli, 2013; Farajzadeh and Zafarani, 2010). Accordingly, it allows us to extend and obtain some existence results for equilibrium-like problems.
In this paper, an extension of the Fan-KKM lemma to Hadamard manifolds is establishe. By using it... more In this paper, an extension of the Fan-KKM lemma to Hadamard manifolds is establishe. By using it some existence results of equilibrium points on Hadamard manifolds are provided. Finally as an application of the main results equilibrium an existence result of a solution of the mixed variational inequality problem in the setting of Hadamard manifolds is stated.
In this paper, $K-$ metric type spaces, generalized KKM mappings, KKM property and fixed point ... more In this paper, $K-$ metric type spaces, generalized KKM mappings, KKM property and fixed point property are introduced. Moreover a relationship between KKM property and fixed point property is established and finally some fixed point theorems $K-$ metric type spaces are presented.
In this paper, a new common fixed point theorem for two mappings which are satisfied the Suzuki’s... more In this paper, a new common fixed point theorem for two mappings which are satisfied the Suzuki’s generalized weak contractive condition in the setting of partially ordered metric spaces is established. Some suitable examples are furnished to demonstrate the validity of the hypotheses of our results and reality of our generalizations. The results of this paper can be viewed as a generalization and improvement of some well-known results in this area.
In this article, some new vectorial versions of Takahashi’s nonconvex minimization theorem, which... more In this article, some new vectorial versions of Takahashi’s nonconvex minimization theorem, which involve algebraic notions instead of topological notions, are established. A nonlinear separation theorem, which extends the result derived by Gerth and Weidner (JAMA 67:297–320, 1990) to general linear spaces (not necessarily endowed with a topology), is proved. Some examples, in order to illustrate and compare the results of this article with the corresponding known results from the literature, are provided.
In this paper, we consider a type of the celebrated convex feasibility problem, named as split qu... more In this paper, we consider a type of the celebrated convex feasibility problem, named as split quasi-convex feasibility problem (SQFP). The SQFP is to find a point in a sublevel set of a quasi-convex function in one space and its image under a bounded linear operator is contained in a sublevel set of another quasi-convex function in the image space. We propose a new adaptive subgradient algorithm for solving SQFP problem. We also discuss the convergence analyses for two cases: the first case where the functions are upper semicontinuous in the setting of finite dimensional, and the second case where the functions are weakly continuous in the infinite-dimensional settings. Finally some numerical examples in order to support the convergence results are given.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017
In this paper, we attempt to define a new KKM map for nonself maps in the setting of Hadamard man... more In this paper, we attempt to define a new KKM map for nonself maps in the setting of Hadamard manifolds, which is then utilized to state the finite intersection property in this framework. Subsequently, this property is used to develop the Fan-KKM theorem for nonself maps on Hadamard manifolds. Moreover, a new definition of upper semicontinuouty and a generalization of the closedness of a set are also proposed. Inspired by this extension, we establish a new existence theorem of a solution to the equilibrium problem for nonself maps on Hadamard Manifolds. As an application of our KKM theorem, we obtain an existence result of maximal elements for nonself set valued mappings in Hadamard manifold frameworks. Finally, for the sake of clarity, a number of examples are presented throughout the paper and our results are compared with the results of some other papers. Keywords Equilibrium problem • Hadamard Manifold • KKM Maps • Maximal elements Mathematics Subject Classification 57p99 • 49J40 Recently, many problems in nonlinear analysis such as convex analysis, fixed point theory, variational inequality and optimization problems are extended from Euclidean spaces B A. P. Farajzadeh
e newest generalization of the Banach contraction through the notions of the generalized F-contra... more e newest generalization of the Banach contraction through the notions of the generalized F-contraction, simulation function, and admissible function is introduced. e existence and uniqueness of fixed points for a self-mapping on complete metric spaces by the new constructed contraction are investigated. e results of this article can be viewed as an improvement of the main results given in the references.
In this paper, the notion of strictly (α, η, ψ, ξ)-contractive multi-valued mappings is introduce... more In this paper, the notion of strictly (α, η, ψ, ξ)-contractive multi-valued mappings is introduced where the continuity of ξ is relaxed. The existence of fixed point theorems for such mappings in the setting of α-η-complete partial metric spaces are provided. The results of the paper can be viewed as the extension of the recent results obtained in the literature. Furthermore, we assure the fixed point theorems in partial complete metric spaces endowed with an arbitrary binary relation and with a graph using our obtained results.
We consider a new class of complementarity problems for η-pseudomonotone maps and obtain an exist... more We consider a new class of complementarity problems for η-pseudomonotone maps and obtain an existence result for their solutions in real Hausdorff topological vector spaces. Our results extend the same previous results in this literature.
Nonlinear functional analysis and applications, Apr 13, 2016
In this paper, we first give a generalization of Takahashi's existence theorem for a vector v... more In this paper, we first give a generalization of Takahashi's existence theorem for a vector valued mapping. From the existence theorem, we establish a generalized Caristi's fixed point theorem and a generalized vector Ekeland's variational principle. As an application, we show that if a differentiable function F with values in a Banach lattice has a order lower bound (although it need not attain it), then for every e> 0, there exists some point u_e, where |F(u_e)|
We introduce a new family of mappings on [0, +∞) by relaxing the nondecreasing condition on the m... more We introduce a new family of mappings on [0, +∞) by relaxing the nondecreasing condition on the mappings and by using the properties of this new family we present some fixed point theorems for-contractive-type mappings in the setting of complete metric spaces. By applying our obtained results, we also assure the fixed point theorems in partially ordered complete metric spaces and as an application of the main results we provide an existence theorem for a nonlinear differential equation.
Journal of Inequalities and Applications, May 2, 2014
Recently Huang et al. (Math. Comput. Model. 43:1267-1274, 2006) introduced a class of parametric ... more Recently Huang et al. (Math. Comput. Model. 43:1267-1274, 2006) introduced a class of parametric implicit vector equilibrium problems (for short PIVEP) and they presented some existence results for a solution of PIVEP. Also, they provided two theorems about upper and lower semi-continuity of the solution set of PIVEP in a locally convex Hausdorff topological vector space. The paper extends the corresponding results obtained in the setting of topological vector spaces with mild assumptions and removing the notion of locally non-positiveness at a point and lower semi-continuity of the parametric mapping.
We first introduce the notion of-upper sign property which is an extension of the upper sign prop... more We first introduce the notion of-upper sign property which is an extension of the upper sign property introduced in Castellani and Giuli, 2013, by relaxing convexity on the set. Afterwards, we establish a link between the solution sets of local dual equilibrium problem (Minty local equilibrium problem) and equilibrium problem for mappings whose domains are not necessarily convex by relaxing the upper sign continuity on the map, as it is assumed in the literature (Bianchi and Pini, 2005; Castellani and Giuli, 2013; Farajzadeh and Zafarani, 2010). Accordingly, it allows us to extend and obtain some existence results for equilibrium-like problems.
In this paper, an extension of the Fan-KKM lemma to Hadamard manifolds is establishe. By using it... more In this paper, an extension of the Fan-KKM lemma to Hadamard manifolds is establishe. By using it some existence results of equilibrium points on Hadamard manifolds are provided. Finally as an application of the main results equilibrium an existence result of a solution of the mixed variational inequality problem in the setting of Hadamard manifolds is stated.
In this paper, $K-$ metric type spaces, generalized KKM mappings, KKM property and fixed point ... more In this paper, $K-$ metric type spaces, generalized KKM mappings, KKM property and fixed point property are introduced. Moreover a relationship between KKM property and fixed point property is established and finally some fixed point theorems $K-$ metric type spaces are presented.
In this paper, a new common fixed point theorem for two mappings which are satisfied the Suzuki’s... more In this paper, a new common fixed point theorem for two mappings which are satisfied the Suzuki’s generalized weak contractive condition in the setting of partially ordered metric spaces is established. Some suitable examples are furnished to demonstrate the validity of the hypotheses of our results and reality of our generalizations. The results of this paper can be viewed as a generalization and improvement of some well-known results in this area.
In this article, some new vectorial versions of Takahashi’s nonconvex minimization theorem, which... more In this article, some new vectorial versions of Takahashi’s nonconvex minimization theorem, which involve algebraic notions instead of topological notions, are established. A nonlinear separation theorem, which extends the result derived by Gerth and Weidner (JAMA 67:297–320, 1990) to general linear spaces (not necessarily endowed with a topology), is proved. Some examples, in order to illustrate and compare the results of this article with the corresponding known results from the literature, are provided.
In this paper, we consider a type of the celebrated convex feasibility problem, named as split qu... more In this paper, we consider a type of the celebrated convex feasibility problem, named as split quasi-convex feasibility problem (SQFP). The SQFP is to find a point in a sublevel set of a quasi-convex function in one space and its image under a bounded linear operator is contained in a sublevel set of another quasi-convex function in the image space. We propose a new adaptive subgradient algorithm for solving SQFP problem. We also discuss the convergence analyses for two cases: the first case where the functions are upper semicontinuous in the setting of finite dimensional, and the second case where the functions are weakly continuous in the infinite-dimensional settings. Finally some numerical examples in order to support the convergence results are given.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017
In this paper, we attempt to define a new KKM map for nonself maps in the setting of Hadamard man... more In this paper, we attempt to define a new KKM map for nonself maps in the setting of Hadamard manifolds, which is then utilized to state the finite intersection property in this framework. Subsequently, this property is used to develop the Fan-KKM theorem for nonself maps on Hadamard manifolds. Moreover, a new definition of upper semicontinuouty and a generalization of the closedness of a set are also proposed. Inspired by this extension, we establish a new existence theorem of a solution to the equilibrium problem for nonself maps on Hadamard Manifolds. As an application of our KKM theorem, we obtain an existence result of maximal elements for nonself set valued mappings in Hadamard manifold frameworks. Finally, for the sake of clarity, a number of examples are presented throughout the paper and our results are compared with the results of some other papers. Keywords Equilibrium problem • Hadamard Manifold • KKM Maps • Maximal elements Mathematics Subject Classification 57p99 • 49J40 Recently, many problems in nonlinear analysis such as convex analysis, fixed point theory, variational inequality and optimization problems are extended from Euclidean spaces B A. P. Farajzadeh
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