Strict Pseudo-contractions Research Articles

New Hybrid Steepest Descent Algorithms for Equilibrium Problem and Infinitely Many Strict Pseudo-Contractions in Hilbert Spaces

We propose an explicit iterative scheme for finding a common element of the set of fixed points of infinitely many strict pseudo-contractive mappings and the set of solutions of an equilibrium problem by the general iterative method, which solves the variational inequality. In the setting of real Hilbert spaces, strong convergence theorems are proved. The results presented in this paper improve and extend the corresponding results reported by some authors recently. Furthermore, two numerical examples are given to demonstrate the effectiveness of our iterative scheme.

Viscosity-Projection Method for a Family of General Equilibrium Problems and Asymptotically Strict Pseudocontractions in the Intermediate Sense

In this paper, a Meir-Keeler contraction is introduced to propose a viscosity-projection approximation method for finding a common element of the set of solutions of a family of general equilibrium problems and the set of fixed points of asymptotically strict pseudocontractions in the intermediate sense. Strong convergence of the viscosity iterative sequences is obtained under some suitable conditions. Results presented in this paper extend and unify the previously known results announced by many other authors.

A General Iterative Algorithm with Strongly Positive Operators for Strict Pseudo-Contractions

This paper deals with a new iterative algorithm{xn}with a strongly positive operatorAfor ak-strict pseudo-contractionTand a non-self-Lipschitzian mappingSin Hilbert spaces. Under certain appropriate conditions, the sequence{xn}converges strongly to a fixed point ofT, which solves some variational inequality. The results here improve and extend some recent related results.

The Split Feasibility Problems for Countable Families of Asymptotically Strict Pseudocontractions

An up-to-date algorithm for solving the split feasibility problem for countable families of asymptotically strict pseudocontractions is introduced in the framework of Hilbert spaces. Our results greatly improve and extend those of other authors whose related research studies are restricted to the situation of at most finitely many such mappings.

Existence and Convergence Theorems by an Iterative Shrinking Projection Method of a Strict Pseudocontraction in Hilbert Spaces

The aim of this paper is to provide some existence theorems of a strict pseudocontraction by the way of a hybrid shrinking projection method, involving some necessary and sufficient conditions. The method allows us to obtain a strong convergence iteration for finding some fixed points of a strict pseudocontraction in the framework of real Hilbert spaces. In addition, we also provide certain applications of the main theorems to confirm the existence of the zeros of an inverse strongly monotone operator along with its convergent results.

A hybrid projection method for solving a common solution of a system of equilibrium problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense in Hilbert spaces

Abstract In this paper, we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding a common solution of a system of equilibrium problems of bifunctions satisfying certain conditions and a common solution of fixed point problems of a family of uniformly Lipschitz continuous and asymptotically λ i -strict pseudocontractive mappings in the intermediate sense. We prove the strong convergence theorem for a new iterative algorithm under some mild conditions in Hilbert spaces. Finally, we also give a numerical example which supports our results. MSC:47H05, 47H09, 47H10.

Weak convergence of algorithms for asymptotically strict pseudocontractions in the intermediate sense and equilibrium problems

In this paper, equilibrium problems and fixed-point problems based on an iterative method are investigated. It is proved that the sequence generated in the purposed iterative process weakly converges to a common element of the fixed-point set of an asymptotically strict pseudocontraction in the intermediate sense and the solution set of a system of equilibrium problems in the framework of real Hilbert spaces. MSC:47H05, 47H09, 47J25, 90C33.

Convergence results for the zero-finding problem and fixed points of nonexpansive semigroups and strict pseudocontractions

In this work, we establish strong convergence theorems for solving the fixed point problem of nonexpansive semigroups and strict pseudocontractions, and the zero-finding problem of maximal monotone operators in a Hilbert space. We further apply our result to the convex minimization problem and commutative semigroups. MSC: 47H09; 47H10

Approximation theorems for solving common solution of a system of mixed equilibrium problems and variational inequality problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense

In this paper, we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding the common solution of a system of mixed equilibrium problems of bifunctions satisfying certain the conditions and the common solution of variational inequality problems of inverse strongly monotone mappings and the common solution of fixed point problems for a family of uniformly Lipschitzian continuous and asymptotically λi-strict pseudocontractive mapping in the intermediate sense. We prove the strong convergence theorem for a new iterative algorithm under some mild conditions in Hilbert spaces. Finally, we also give some numerical examples for support our results.

An Iterative Scheme for Generalized Equilibrium Problems and Fixed Point Problems of Strict Pseudo-Contraction Mappings

An Iterative Scheme for Generalized Equilibrium Problems and Fixed Point Problems of Strict Pseudo-Contraction Mappings

STRONG CONVERGENCE OF AN ITERATIVE ALGORITHM FOR SYSTEMS OF VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS IN q-UNIFORMLY SMOOTH BANACH SPACES

In this paper, we introduce a new iterative scheme to investigate the problem of nding a common element of nonexpansive mappings and the set of solutions of generalized variational inequalities for a <TEX>$k$</TEX>-strict pseudo-contraction by relaxed extra-gradient methods. Strong convergence theorems are established in <TEX>$q$</TEX>-uniformly smooth Banach spaces.

Approximation of common solutions of variational inequalities via strict pseudocontractions

In this paper, a convex feasibility problem is considered. We construct an iterative method to approximate a common element of the solution set of classical variational inequalities and of the fixed point set of a strict pseudocontraction. Strong convergence theorems for the common element are established in the framework of Hilbert spaces.

A HYBRID PROJECTION METHOD FOR RELAXED COCOERCIVE MAPPINGS AND STRICTLY PSEUDO-CONTRACTIVE MAPPINGS

The purpose of this paper is to introduce a hybrid projection method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inclusion problem and the set of common fixed points of a finite family of strict pseudo-contractions in Hilbert spaces.

Strong convergence of a hybrid projection iterative algorithm for common solutions of operator equations and of inclusion problems

In this article, zero points of the sum of a maximal monotone operator and an inverse-strongly monotone mapping, solutions of a monotone variational inequality, and fixed points of a strict pseudocontraction are investigated. A hybrid projection iterative algorithm is considered for analyzing the convergence of the iterative sequences. Strong convergence theorems are established in the framework of real Hilbert spaces without any compact assumptions. Some applications of the main results are also provided. AMS Classification: 47H05; 47H09; 47J25; 90C33.

The extragradient-Armijo method for pseudomonotone equilibrium problems and strict pseudocontractions

In this article, we present a new iteration method for finding a common element of the set of fixed points of p strict pseudocontractions and the set of solutions of equilibrium problems for pseudomonotone bifunctions without Lipschitz-type continuous conditions. The iterative process is based on the extragradient method and Armijo-type linesearch techniques. We obtain weak convergence theorems for the sequences generated by this process in a real Hilbert space.AMS 2010 Mathematics Subject Classification: 65 K10; 65 K15; 90 C25; 90 C33.

RELAXED PROJECTION-VISCOSITY APPROXIMATION METHOD

The purpose of this paper is to investigate the problem of finding a common element of the solution set of a general system of variational inequalities, the solution set of a variational inequality problem and the fixed point set of a strict pseudocontraction in a real Hilbert space. Based on the well-known viscosity approximation method, extragradient method and Mann's iteration method, we propose and analyze a relaxed projection-viscosity approximation method for computing a common element. Under very mild assumptions, we obtain a strong convergence theorem for three sequences generated by the proposed method. Our proposed method is quite general and flexible and develops some iterative methods considered in the earlier and recent literature.

Iterative methods for variational inequality problems and fixed point problems of a countable family of strict pseudo-contractions in a q-uniformly smooth Banach space

In this article, we introduce iterative methods (implicit and explicit) for finding a common fixed point set of a countable family of strict pseudo-contractions, which is a unique solution of some variational inequality. Furthermore, we prove the strong convergence theorems of such iterative scheme in a q-uniformly smooth Banach space which admits a weakly sequentially continuous generalized duality mapping. The results presented in this article extend and generalize the corresponding results announced by Yamada and Ceng et al. from Hilbert spaces to Banach spaces. Mathematics Subject Classification 2010: 47H09; 47J05; 47J20; 65J15.

Generalized extragradient iterative method for systems of variational inequalities

Abstract The purpose of this article is to investigate the problem of finding a common element of the solution sets of two different systems of variational inequalities and the set of fixed points a strict pseudocontraction mapping defined in the setting of a real Hilbert space. Based on the well-known extragradient method, viscosity approximation method and Mann iterative method, we propose and analyze a generalized extra-gradient iterative method for computing a common element. Under very mild assumptions, we obtain a strong convergence theorem for three sequences generated by the proposed method. Our proposed method is quite general and flexible and includes the iterative methods considered in the earlier and recent literature as special cases. Our result represents the modification, supplement, extension and improvement of some corresponding results in the references. Mathematics Subject Classification (2000): Primary 49J40; Secondary 65K05; 47H09.

Strong convergence of a new general iterative method for variational inequality problems in Hilbert spaces

Abstract In this article, we introduce a new iterative scheme with Meir-Keeler contractions for strict pseudo-contractions in Hilbert spaces. We also discuss the strong convergence theorems of the new iterative scheme for variational inequality problems in Hilbert spaces. The methods in this article are interesting and are different from those given in many other articles. Our results improve and extend the corresponding results announced by many others. MR(2000) Subject Classification: 47H09; 47H10.

Studies on Common Solutions of a Variational Inequality and a Fixed-Point Problem

In this paper, we construct a new projection method and prove the strong convergence for finding a common element of a set of fixed points of strict pseudo-contractions and a set of solutions of a variational inequality with inverse strongly monotone mappings in the setting of real Hilbert spaces. Our results improve and extend the recent results by Huang, Noor, and Al-Said (J. Optim. Theory Appl. 147(1):194–204, 2010), Takahashi and Toyoda (J. Optim. Theory Appl. 118(2):417–428, 2003).