FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS

doi:10.1016/S0252-9602(16)30049-2

摘要/Abstract

摘要：

The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set Ω of the split feasibility problem and the set F(T) of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p-uniformly convex Banach spaces which are also uniformly smooth. By combining Mann's iterative method and the Halpern's approximation method, we propose an iterative algorithm for finding an element of the set F(T)∩Ω; moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.

关键词: strong convergence, split feasibility problem, uniformly convex, uniformly smooth, fixed point problem, right Bregman strongly nonexpansive mappings

Abstract:

Key words: strong convergence, split feasibility problem, uniformly convex, uniformly smooth, fixed point problem, right Bregman strongly nonexpansive mappings

中图分类号:

49J53

Y. SHEHU, O. T. MEWOMO, F. U. OGBUISI. FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS[J]. 数学物理学报(英文版), 2016, 36(3): 913-930.

Y. SHEHU, O. T. MEWOMO, F. U. OGBUISI. FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS[J]. Acta mathematica scientia,Series B, 2016, 36(3): 913-930.

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