A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given

Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications

AbstractIn this paper, we consider the problem of convergence of an iterative algorithm for a system of generalized variational inequalities and a nonexpansive mapping. Strong convergence theorems are established in the framework of real Banach spaces

Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi--Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces

The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi--asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors

Convergence and stability of iterative algorithm for a new system of (A,η)-accretive mapping inclusions in Banach spaces

AbstractIn this paper, we introduce and study a new system of (A,η)-accretive mapping inclusions in Banach spaces. Using the resolvent operator associated with (A,η)-accretive mappings, we suggest a new general algorithm and establish the existence and uniqueness of solutions for this system of (A,η)-accretive mapping inclusions. Under certain conditions, we discuss the convergence and stability of iterative sequence generated by the algorithm. Our results extend, improve and unify many known results on variational inequalities and variational inclusions