Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings

Abstract

In this paper, we consider a new parallel algorithm combining viscosity approximation methods to approximate the multiple-set split common fixed point problem governed by demicontractive mappings, and get the generated sequence converges strongly to a solution of this problem. The results obtained in this paper generalize and improve the recent ones announced by many others. c 2017 All rights reserved.Keywords: Multiple-set split equality common fixed-point problem, demicontractive mapping, strong convergence. 2010 MSC: 47H09, 47H10, 47J05, 54H25.

Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces

“…Several authors have considered this problem for finite families of mappings (see e.g. [29,36]) and infinte families (see [10]).…”

“…In 2017, Wang et al [29] studied the MSECFP (10) for demicontractive mappings. They proposed the following viscosity iterative algorithm and obtained some strong convergence results for solving the MSECFP (10) and the SEFPP (5) under some mild conditions.…”

“…et al [29] properly contains the class of mappings considered in Zhao et al [34]. Also, the algorithm proposed by Wang et al [29] yields strong convergence which is more suitable in application than weak convergence. However, the algorithm cannot work for general quasi-pseudocontractive mappings.…”

“…Secondly, the condition given in [29] Theorem 3.3 (iii) is not applicable in the case of quasi-pseudocontractive mappings. The following question then comes: Is it possible to construct a viscosity iterative algorithm for multiple-sets split equality common fixed point problem for quasi-pseudocontractive mappings?…”

“…Inspired and motivated by the works of Wang et al [29] and Chang et al [7], we propose a viscosity iterative algorithm for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings which is more general than the class of quasi-nonexpansive mappings, directed mappings and demicontractive mappings. Our algorithm is constructed in such a way that the stepsize γ n does not require a prior estimate of the norm of bounded linear operators.…”