Abstract
Mann-like iteration methods are significant to deal with convex feasibility problems in Banach spaces. We focus on a relaxed Mann implicit iteration method to solve a general system of accretive variational inequalities with an asymptotically nonexpansive mapping in the intermediate sense and a countable family of uniformly Lipschitzian pseudocontractive mappings. More convergence theorems are proved under some suitable weak condition in both 2-uniformly smooth and uniformly convex Banach spaces.
Highlights
Throughout this article, E will be supposed to be a real Banach space and E∗ stands for its ∗topological dual
E is said to be a uniformly smooth Banach space if the above limit is uniformly achieved for all x, y ∈ USE
The relaxed Mann implicit iteration method presented in this paper is from both the Mann iteration and the Korpelevich’s extragradient iteration
Summary
Throughout this article, E will be supposed to be a real Banach space and E∗ stands for its. E is said to be a uniformly smooth Banach space if the above limit is uniformly achieved for all x, y ∈ USE. Invoke that the operator f is said to be δ-Lipschitzian continuous in the set C if k f ( x ) − f (y)k ≤ δk x − yk,. Becomes the GSVI considered in [23], which includes as special cases the problems arising, especially from linear or nonlinear complementary problems, and quadratic convex programming It has no doubt the system of variational inequalities has played a crucial role on both theoretical and applied sciences. We introduce a relaxed Mann-like iteration method for the approximation of solutions of the GSVI (3) in both 2-uniformly smooth and uniformly convex Banach setting. The relaxed Mann implicit iteration method presented in this paper is from both the Mann iteration and the Korpelevich’s extragradient iteration
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