Abstract
In this paper, we study the split feasibility problem in Banach spaces. At first, we prove that a solution of this problem is a solution of the equivalent equation defined by using a metric projection, a generalized projection, and sunny generalized nonexpansive retraction, respectively. Then, using the hybrid method with these projections, we prove strong convergence theorems in mathematical programing in order to find a solution of the split feasibility problem in Banach spaces.
Highlights
Bregman proposed a generalization for the cyclic metric projection method of computing points in the intersection of linear closed subspaces of a Hilbert space in [1], invented by von Neumann [2]
We prove that a solution of this problem is a solution of the equivalent equation defined by using a metric projection, a generalized projection, and sunny generalized nonexpansive retraction, respectively
Alber and Butnariu achieve distinction of the study of this Bregman projection and the result of the properties. They used this cyclic Bregman projection method for finding the solution of the consistent convex feasibility problem of computing a common point of the closed convex subspaces in a reflexive Banach space [3]
Summary
Bregman proposed a generalization for the cyclic metric projection method of computing points in the intersection of linear closed subspaces of a Hilbert space in [1], invented by von Neumann [2]. Alber and Butnariu achieve distinction of the study of this Bregman projection and the result of the properties They used this cyclic Bregman projection method for finding the solution of the consistent convex feasibility problem of computing a common point of the closed convex subspaces in a reflexive Banach space [3]. Using the methods with metric projections in mathematical programing, they showed strong convergence theorems for finding a solution of the split feasibility problem. For uniformly convex and smooth Banach spaces E and F, we study the split feasibility problem of a bounded linear operator A from E to F. Using the hybrid methods with these projections, we prove the strong convergence theorems in mathematical programing in order to find a solution of the split feasibility problem in Banach spaces
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