ABSTRACT In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings... more ABSTRACT In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorem for finding common fixed points with the set of solutions of an equilibrium problem.
ABSTRACT Recently, Samet et al. (2012) introduced the notion of --contractive mappings and establ... more ABSTRACT Recently, Samet et al. (2012) introduced the notion of --contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weak --contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.
Abstract—By using an implicit Iteration and selector theorems one can prove some new random fixed... more Abstract—By using an implicit Iteration and selector theorems one can prove some new random fixed point theorems for some wide classes of multivalued nonlinear random mappings. It seems t hat by this approach, the proofs are simple enough.
ABSTRACT We introduce a new iterative algorithm for finding a common element of the set of soluti... more ABSTRACT We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others.
ABSTRACT We introduce a new iterative method for finding a common element of the set of solutions... more ABSTRACT We introduce a new iterative method for finding a common element of the set of solutions for a mixed equilibrium problem, the set of solutions of a variational inequality for a β-inverse-strongly monotone mapping, and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Cesàro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Kumam and Katchang (2009), Peng and Yao (2009), Shimizu and Takahashi (1997), and some other authors.
Kirk and Xu introduced the concept of asymptotic pointwise contractions. In this paper, we invest... more Kirk and Xu introduced the concept of asymptotic pointwise contractions. In this paper, we investigate these kinds of mappings in modular spaces. Moreover, the fixed point theorem for asymptotic pointwise nonexpansive mappings in modular spaces is also studied. The results of this paper improve and extend the results of Razani et al. [A. Razani, E. Nabizadeh, M. Beyg Mohamadi, S.
We present an iterative method for fixed point problems, generalized mixed equilibrium problems, ... more We present an iterative method for fixed point problems, generalized mixed equilibrium problems, and variational inequality problems. Our method is based on the so-called viscosity hybrid steepest descent method. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of generalized mixed equilibrium problems, and the set of solutions of variational inequality problems for a relaxed cocoercive mapping in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality. The results presented in this paper generalize and extend some well-known strong convergence theorems in the literature.
ABSTRACT The purpose of this paper is to investigate the problem of finding a common element of t... more ABSTRACT The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new iterative scheme for finding the common element of the above three sets. Our results improve and extend the corresponding results of the works by Zhang et al. (2008), Peng et al. (2008), Peng and Yao (2009), as well as Plubtieng and Sriprad (2009) and some well-known results in the literature.
ABSTRACT We prove strong convergence of modified hybrid projection methods for finding a common e... more ABSTRACT We prove strong convergence of modified hybrid projection methods for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of the variational inequality of an inverse strongly monotone operator, the zero point of a maximal monotone operator and the set of fixed points of two relatively quasi-nonexpansive mappings in a Banach space. Our results modify and improve the recently announced ones by many authors.
ABSTRACT In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings... more ABSTRACT In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorem for finding common fixed points with the set of solutions of an equilibrium problem.
ABSTRACT Recently, Samet et al. (2012) introduced the notion of --contractive mappings and establ... more ABSTRACT Recently, Samet et al. (2012) introduced the notion of --contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weak --contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.
Abstract—By using an implicit Iteration and selector theorems one can prove some new random fixed... more Abstract—By using an implicit Iteration and selector theorems one can prove some new random fixed point theorems for some wide classes of multivalued nonlinear random mappings. It seems t hat by this approach, the proofs are simple enough.
ABSTRACT We introduce a new iterative algorithm for finding a common element of the set of soluti... more ABSTRACT We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others.
ABSTRACT We introduce a new iterative method for finding a common element of the set of solutions... more ABSTRACT We introduce a new iterative method for finding a common element of the set of solutions for a mixed equilibrium problem, the set of solutions of a variational inequality for a β-inverse-strongly monotone mapping, and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Cesàro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Kumam and Katchang (2009), Peng and Yao (2009), Shimizu and Takahashi (1997), and some other authors.
Kirk and Xu introduced the concept of asymptotic pointwise contractions. In this paper, we invest... more Kirk and Xu introduced the concept of asymptotic pointwise contractions. In this paper, we investigate these kinds of mappings in modular spaces. Moreover, the fixed point theorem for asymptotic pointwise nonexpansive mappings in modular spaces is also studied. The results of this paper improve and extend the results of Razani et al. [A. Razani, E. Nabizadeh, M. Beyg Mohamadi, S.
We present an iterative method for fixed point problems, generalized mixed equilibrium problems, ... more We present an iterative method for fixed point problems, generalized mixed equilibrium problems, and variational inequality problems. Our method is based on the so-called viscosity hybrid steepest descent method. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of generalized mixed equilibrium problems, and the set of solutions of variational inequality problems for a relaxed cocoercive mapping in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality. The results presented in this paper generalize and extend some well-known strong convergence theorems in the literature.
ABSTRACT The purpose of this paper is to investigate the problem of finding a common element of t... more ABSTRACT The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new iterative scheme for finding the common element of the above three sets. Our results improve and extend the corresponding results of the works by Zhang et al. (2008), Peng et al. (2008), Peng and Yao (2009), as well as Plubtieng and Sriprad (2009) and some well-known results in the literature.
ABSTRACT We prove strong convergence of modified hybrid projection methods for finding a common e... more ABSTRACT We prove strong convergence of modified hybrid projection methods for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of the variational inequality of an inverse strongly monotone operator, the zero point of a maximal monotone operator and the set of fixed points of two relatively quasi-nonexpansive mappings in a Banach space. Our results modify and improve the recently announced ones by many authors.
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