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

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 map-pings in uniformly convex Banach spaces. In addition, we apply our result to solve a convex-constrained minimization problem, vari-ational 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 ob-tained results in this paper improve and extend some related results in the literature.