A New Iterative Method for Solving Constrained Minimization, Variational Inequality and Split Feasibility Problems in the Framework of Banach Spaces

Abstract

In this paper, we introduce a new type of modified generalized $\alpha$-nonexpansive mapping and establish some fixed point properties and demiclosedness principle for this class of mappings in the framework of uniformly convex Banach spaces. We further propose a new iterative method for approximating a common fixed point of two modified generalized $\alpha$-nonexpansive mappings and present some weak and strong convergence theorems for these mappings in uniformly convex Banach spaces. In addition, we apply our result to solve a convex-constrained minimization problem, variational inequality and split feasibility problem and present some numerical experiments in infinite dimensional spaces to establish the applicability and efficiency of our proposed algorithm. The obtained results in this paper improve and extend some related results in the literature.

Keywords

• modified generalized $\alpha$-nonexpansive mapping
• variational inequality problem
• fixed point
• iterative scheme