A Shrinking Projection Algorithm with Errors for Costerro Bounded Linear Mappings

Joseph Frank Gordon

doi:10.1155/2020/7052349

Abstract

The purpose of this paper is to introduce and analyze the shrinking projection algorithm with errors for a finite set of costerro bounded linear mappings in the setting of uniformly convex smooth Banach spaces. Here, under finite dimensional or compactness restriction or the error term being zero, the strong limit point of the sequence stated in the iterative scheme for these mappings in uniformly convex smooth Banach spaces was studied. This paper extends Ezearn and Prempeh’s result for nonexpansive mappings in real Hilbert spaces.

Highlights

Fixed-point theory is a fascinating subject, with a lot of applications in various fields of mathematics and engineering
For more information on the fixed-point problem and its applications to certain types of linear and nonlinear problems, interested readers should be referred to Tang and Chang [3], Solodov and Svaiter [4], Takahashi [5, 6], and Blum and Oettli [7]
Finding an exact closed form of a solution to a fixed-point problem is almost a difficult task. It has been of particular importance in the development of feasible iterative schemes or methods for approximating fixed points of certain maps, most notably, nonexpansive type of mappings

Summary

Introduction

Fixed-point theory is a fascinating subject, with a lot of applications in various fields of mathematics and engineering. At is to say that the convergence of the iterative sequence in the scheme presented in Yasunori’s paper, that is, the error term ε0 0 is independent of the boundedness of the closed convex subset in a real Hilbert space. Let X be a smooth Banach space and let X∗ be the dual space of X. e generalised projection functional φ(·, ·): X × X ⟶ R is defined by φ(y, x) ‖y‖2 − 2R〈y, Jx〉 +‖x‖2, (5)

Results

Conclusion