System Of Mixed Equilibrium Problems Research Articles

WEAK AND STRONG CONVERGENCE THEOREMS FOR A SYSTEM OF MIXED EQUILIBRIUM PROBLEMS AND A NONEXPANSIVE MAPPING IN HILBERT SPACES

In this paper, we introduce an iterative sequence for finding solution of a system of mixed equilibrium problems and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Then, the weak and strong convergence theorems are proved under some parameters control- ling conditions. Moreover, we apply our result to fixed point problems, system of equilibrium problems, general system of variational inequal- ities, mixed equilibrium problem, equilibrium problem and variational inequality.

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 algorithm for common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings with optimization problems

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a variational inclusion problems for inverse strongly monotone mappings, the set of common fixed points for nonexpansive semigroups and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (Appl Math Comput 216:51---60, 2010), Hao (Appl Math Comput 217(7):3000---3010, 2010), Jaiboon and Kumam (Nonlinear Anal 73:1180---1202, 2010) and many others.

The hybrid algorithm for the system of mixed equilibrium problems, the general system of finite variational inequalities and common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings

In this article, we introduce a new iterative algorithm by the shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of general system of finite variational inequalities, the set of solutions of fixed points for nonexpansive semigroups and the set of common fixed points for an infinite family of strictly pseudo-contractive 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. Our results improve and extend the corresponding recent results in literature work.

The System of Mixed Equilibrium Problems for Quasi‐Nonexpansive Mappings in Hilbert Spaces

We first introduce the iterative procedure to approximate a common element of the fixed‐point set of two quasinonexpansive mappings and the solution set of the system of mixed equilibrium problem (SMEP) in a real Hilbert space. Next, we prove the weak convergence for the given iterative scheme under certain assumptions. Finally, we apply our results to approximate a common element of the set of common fixed points of asymptotic nonspreading mapping and asymptotic TJ mapping and the solution set of SMEP in a real Hilbert space.

Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed‐Point Problems, and Variational Inclusions with Application to Minimization Problem

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for a β‐inverse‐strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

An Iterative Method for Solving a System of Mixed Equilibrium Problems, System of Quasivariational Inclusions, and Fixed Point Problems of Nonexpansive Semigroups with Application to Optimization Problems

We introduce a general implicit iterative scheme base on viscosity approximation method with a ϕ‐strongly pseudocontractive mapping for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for a nonexpansive semigroup, and the set of solutions of system of variational inclusions with set‐valued maximal monotone mapping and Lipschitzian relaxed cocoercive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator.

A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010) and many others.

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.

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.

A system of mixed equilibrium problems, fixed point problems of strictly pseudo-contractive mappings and nonexpansive semi-groups

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for an infinite family of strictly pseudo-contractive mappings and the set of common fixed points for nonexpansive semi-groups in Hilbert space. Under suitable conditions some strong convergence theorem are proved. The results presented in the paper extend and improve some recent results.

Weak Convergence Theorems for a System of Mixed Equilibrium Problems and Nonspreading Mappings in a Hilbert Space

We introduce an iterative sequence and prove a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a quasi-nonexpansive mapping in Hilbert spaces. Moreover, we apply our result to obtain a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a nonspreading mapping. The result obtained in this paper improves and extends the recent ones announced by Moudafi (2009),Iemoto and Takahashi (2009), and many others. Using this result, we improve and unify several results in fixed point problems and equilibrium problems.

An algorithm for finding a common solution for a system of mixed equilibrium problem, quasi-variational inclusion problem and fixed point problem of nonexpansive semigroup

In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.

An Algorithm for Finding a Common Solution for a System of Mixed Equilibrium Problem, Quasivariational Inclusion Problem, and Fixed Point Problem of Nonexpansive Semigroup

We introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for nonexpansive semigroup, and the set of solutions of the quasi-variational inclusion problem with multivalued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results announced by some authors.