The Split Equality Fixed Point Problem of Demicontractive Operators with Numerical Example and Application

Yaqin Wang,Jinzuo Chen,Ariana Pitea

doi:10.3390/sym12060902

Abstract

This paper aims to propose a new reckoning method for solving the split equality fixed point problem of demicontractive operators in Hilbert spaces, and to establish a theorem with regard to the strong convergence of this new scheme. As an application, we also consider quasi-pseudo-contractive operators and obtain a result on the solution to the split equality fixed point problem in the framework of Hilbert spaces. A numerical example is also provided.

Highlights

IntroductionThe split feasibility problem (SFP) appeared first in 1994, in a work of Censor and Elfving [1]; it refers to determining an element in the set
The split common fixed point problem (SCFP) appeared in a paper of Censor and Segal [5]; it refers to determining a point x satisfying x ∈ F (S) so that A x ∈ F ( T ), (1)
We study the SEFP (2), a generalization of the SCFP (1)

Summary

Introduction

The split feasibility problem (SFP) appeared first in 1994, in a work of Censor and Elfving [1]; it refers to determining an element in the set. Signal processing and the reconstruction of images have benefited by the development of iterative methods for solving the SFP; see [2,3,4]. The split common fixed point problem (SCFP) appeared in a paper of Censor and Segal [5]; it refers to determining a point x satisfying x ∈ F (S) so that A x ∈ F ( T ), (1). The reconstruction of images or the radio-therapy have used, as a beneficial tool, the SCFP (1) [6,7,8,9,10,11,12,13,14]

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Conclusion