The Split Hierarchical Monotone Variational Inclusions Problems and Fixed Point Problems for Nonexpansive Semigroup
نویسندگان
چکیده
The purpose of this paper is to study a split hierarchical monotone variational inclusion problem which includes split variational inequality problems, split common fixed point problems, split monotone variational inclusion problems, split convex minimization problems, etc., as special cases, and fixed point problems for nonexpansive semigroup in the setting of Hilbert spaces. For solving this kind problems, some new iterative algorithms are proposed. Under suitable conditions, some weak and strong convergence theorems for the sequences generated by the proposed algorithms are proved. The results presented in the paper improve and extend some recent corresponding results. Mathematics Subject Classifications: 47H09, 47J25
منابع مشابه
Explicit Hierarchical Fixed Point Approach to Variational Inequalities
Abstract: An explicit hierarchical fixed point algorithm is introduced to solve monotone variational inequalities, which are governed by a pair of nonexpansive mappings, one of which is used to define the governing operator and the other to define the feasible set. These kinds of variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed po...
متن کاملOn Fixed Point Results for Hemicontractive-type Multi-valued Mapping, Finite Families of Split Equilibrium and Variational Inequality Problems
In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multi-valued hemicontractive-type mapping, the set of common solutions of a finite family of split equilibrium problems and the set of common solutions of a finite family of variational inequality problems in real Hilbert spaces. Moreover, the sequence generated by the proposed algori...
متن کاملA 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. Further...
متن کامل