Strict Pseudo-contractions Research Articles

Hybrid extragradient methods for asymptotically strict pseudo-contractions in the intermediate sense and variational inequality problems

This article is devoted to investigating a new hybrid extragradient method for an asymptotically strict pseudo-contraction in the intermediate sense S and a monotone and Lipschitz continuous mapping A in a Hilbert space. The main purpose is to use this iterative method to generate a sequence for approximating a common element of the fixed point set of S and the solution set of the variational inequality problem for A. Weak convergence and strong convergence for the related sequences are established with respective iteration processes.

Common fixed points of strict pseudocontractions by iterative algorithms

In this paper, we present iteration schemes to weakly and strongly approximate common fixed points of a finite family of a class of strict pseudocontractions.

On a Generalized Ky Fan Inequality and Asymptotically Strict Pseudocontractions in the Intermediate Sense

In this paper, two iterative algorithms are considered for a generalized Ky Fan inequality and a fixed point problem of asymptotically strict pseudocontractions in the intermediate sense. Strong and weak convergence theorems are established in real Hilbert spaces.

A GENERAL ITERATIVE ALGORITHM COMBINING VISCOSITY METHOD WITH PARALLEL METHOD FOR MIXED EQUILIBRIUM PROBLEMS FOR A FAMILY OF STRICT PSEUDO-CONTRACTIONS y

The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of -strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of -strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.

A New Hybrid Algorithm for a System of Mixed Equilibrium Problems, Fixed Point Problems for Nonexpansive Semigroup, and Variational Inclusion Problem

AbstractThe purpose of this paper is to consider a shrinking projection method for finding the common element of the set of common fixed points for nonexpansive semigroups, the set of common fixed points for an infinite family of a "Equation missing"-strict pseudocontraction, the set of solutions of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion problem. Strong convergence of the sequences generated by the proposed iterative scheme is obtained. The results presented in this paper extend and improve some well-known results in the literature.

Strong Convergence by a Hybrid Algorithm for Finding a Common Fixed Point of Lipschitz Pseudocontraction and Strict Pseudocontraction in Hilbert Spaces

We prove a strong convergence theorem by using a hybrid algorithm in order to find a common fixed point of Lipschitz pseudocontraction and κ‐strict pseudocontraction in Hilbert spaces. Our results extend the recent ones announced by Yao et al. (2009) and many others.

An Application of Hybrid Steepest Descent Methods for Equilibrium Problems and Strict Pseudocontractions in Hilbert Spaces

We use the hybrid steepest descent methods for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudocontraction mapping in the setting of real Hilbert spaces. We proved strong convergence theorems of the sequence generated by our proposed schemes.

Approximating Fixed Points of Asymptotically Strict Pseudo-Contraction by Ishikawa's Iteration Algorithm

Approximating Fixed Points of Asymptotically Strict Pseudo-Contraction by Ishikawa's Iteration Algorithm

Strong Convergence Theorems of Modified Ishikawa Iterative Method for an Infinite Family of Strict Pseudocontractions in Banach Spaces

We introduce a new modified Ishikawa iterative process and a new W‐mapping for comput‐ ing fixed points of an infinite family of strict pseudocontractions mapping in the framework of q‐uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent results of Cai and Hu 2010, Dong et al. 2010, Katchang and Kumam 2011 and many others in the literature.

Strong Convergence Theorems for an Infinite Family of Equilibrium Problems and Fixed Point Problems for an Infinite Family of Asymptotically Strict Pseudocontractions

We prove a strong convergence theorem for an infinite family of asymptotically strict pseudo-contractions and an infinite family of equilibrium problems in a Hilbert space. Our proof is simple and different from those of others, and the main results extend and improve those of many others.

Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set‐valued maximal monotone mappings and inverse‐strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was obtained. Our results improve and extend the corresponding results of Martinez‐Yanes and Xu (2006), Shehu (2011), Zhang et al. (2008), and many authors.

Approximation of Common Solutions to System of Mixed Equilibrium Problems, Variational Inequality Problem, and Strict Pseudo-Contractive Mappings

AbstractWe introduce an iterative algorithm for finding a common element of the set of fixed points of strict pseudocontractions mapping, the set of common solutions of a system of two mixed equilibrium problems and the set of common solutions of the variational inequalities with inverse strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. Finally, we apply our results for solving convex feasibility problems in Hilbert spaces. Our results improve and extend the corresponding results announced by many others recently.

Convergence Analysis for a System of Generalized Equilibrium Problems and a Countable Family of Strict Pseudocontractions

We introduce a new iterative algorithm for a system of generalized equilibrium problems and a countable family of strict pseudocontractions in Hilbert spaces. We then prove that the sequence generated by the proposed algorithm converges strongly to a common element in the solutions set of a system of generalized equilibrium problems and the common fixed points set of an infinitely countable family of strict pseudocontractions.

Convergence of Iterative Sequences for Fixed Point and Variational Inclusion Problems

AbstractAn iterative process is considered for finding a common element in the fixed point set of a strict pseudocontraction and in the zero set of a nonlinear mapping which is the sum of a maximal monotone operator and an inverse strongly monotone mapping. Strong convergence theorems of common elements are established in real Hilbert spaces.

STRONG CONVERGENCE OF AN IMPLICIT ITERATIVE PROCESS FOR AN INFINITE FAMILY OF STRICT PSEUDOCONTRACTIONS

In this paper, we consider an implicit iterative process with errors for an in nite family of strict pseudocontractions. Strong convergence theorems are established in the framework of Banach spaces. The results presented in this paper improve and extend the recent ones announced by many others.

WEAK AND STRONG CONVERGENCE THEOREMS OF A MANN-TYPE ITERATIVE ALGORITHM FOR k-STRICT PSEUDO-CONTRACTIONS

In this paper, we consider a Mann-type iterative algorithm for nonself strict pseudo-contractions. Weak and strong convergence theorems are established in the framework of Hilbert spaces. The results presented in this paper improve and extend the results announced by many others.

Strong convergence of a new iterative scheme for a finite family of strict pseudo-contractions

The purpose of this paper is to introduce a new iterative scheme for finding a common fixed point of a finite family of strict pseudo-contractions. The results obtained in this paper extend and improve the corresponding results of Marino, Colao, Qin and Kang [G. Marino, V. Colao, X. Qin, S. M. Kang, Strong convergence of the modified Mann iterative method for strict pseudo-contractions, Comput. Math. Appl. 57 (2009) 455–465].

Theorems of strong convergence of mixed iterative methods for obtaining strict pseudocontractions in Banach spaces

In this work, theorems of strong convergence of a mixed iteration scheme within the viscosity approximation methods for obtaining λ -strict pseudocontractions are established in p -uniformly convex Banach spaces with uniformly Gâteaux differentiable norm. The main result extends various results existing in the current literature.

Convergence theorems for λ-strict pseudo-contractions in q-uniformly smooth Banach spaces

In this paper, we continue to discuss the properties of iterates generated by a strict pseudocontraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336–349 (2007)]. In order to get a strong convergence theorem, we modify the normal Mann’s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.: Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51–60 (2005)] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces.

Strong convergence of an iterative algorithm for an infinite family of strict pseudo-contractions in Banach spaces

In this paper, we introduce a new W-mapping and present an iterative algorithm for an infinite family of strict pseudo-contractions. Strong convergence theorems are proved in Banach spaces. Our results improve and extend the corresponding result announced by Cai and Hu [G. Cai, C. Hu, Strong convergence theorems of modified Ishikawa iterative process with errors for an infinite family of strict pseudo-contractions, Nonlinear Anal. 71(12) (2009) 6044–6053].