Abstract
The purpose of this paper is to introduce a general iterative method for finding solutions of a general system of variational inclusions with Lipschitzian relaxed cocoercive mappings. Strong convergence theorems are established in strictly convex and 2-uniformly smooth Banach spaces. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of strict pseudo-contraction mappings.
Highlights
1.2 t→0 t exists for all x, y ∈ UE
In this paper, motivated by Qin et al 16, Moudafi 18, Marino and Xu, and Qin et al, we introduce a general iterative approximation method for finding common elements of the set of solutions to a general system of variational inclusions 1.11 with Lipschitzian and relaxed cocoercive mappings and the set common fixed points of a countable family of strict pseudocontractions
We prove the strong convergence theorems of such iterative scheme for finding a common element of such two sets which is a unique solution of some variational inequality and is the optimality condition for some minimization problems in strictly convex and 2-uniformly smooth Banach spaces
Summary
Reich 11 extended Browder’s result to the setting of Banach spaces and proved that, if E is a uniformly smooth Banach space, xt converges strongly to a fixed point of T , and the limit defines the unique sunny nonexpansive retraction from C onto F T . Let E be a uniformly smooth Banach space and T : C → C a nonexpansive mapping such that F T / ∅.
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