Multiple-Sets Split Common Fixed-Point Problems for Demicontractive Mappings

Abstract

In this paper, we are concerned with the multiple-sets split common fixed-point problems whenever the involved mappings are demicontractive. We first study several properties of demicontractive mappings and particularly their connection with directed mappings. By making use of these properties, we propose some new iterative methods for solving multiple-sets split common fixed-point problems, as well as multiple-sets spit feasibility problems. Under mild conditions, we establish their weak convergence of the proposed methods.

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

“…For other important recent results regarding the study of the SCFP problem with its particular instances (FPP, SFP, CFP etc. ), we refer the readers to Boikanyo [43], Chen [44], Chen et al [45], Chidume et al [46] (which deals with the split equality fixed-point problem, a generalization of the split feasibility problem), Cui [47], Cui et al [48], Cui and Wang [49,50], Dang et al [51], Eslamian [52,53], Eslamian et al [54], Fan et al [55], Gupta et al [56], Hanjing and Suantai [57][58][59][60], He et al [61][62][63][64], Jailoka and Suantai [65,66], Jirakitpuwapat et al [67], Kitkuan et al [68], Mouktonglang and Suparatulatorn [69], Padcharoen et al [70], Qin and Wang [71], Shehu [72], Shehu and Cholamjiak [73], Shehu and Mewomo [74], Suparatulatorn et al [75,76], Su and Zhao [77], Tang et al [20,78], Wang [79], Wang and Zhao [80], Wang and Cui [29], Wang and Fang [81,82], Wang et al [83]…”

"Approximating fixed points of demicontractive mappings via the quasi-nonexpansive case"

“…As demicontractive mappings constitute one of the most general classes of nonexpansive type mappings with important applications for which the fixed points can be obtained by iterative schemes, there was and still is a great interest in studying their properties, see [2], [4], [27]- [38], [44]- [61], [65]- [79] and most of the references therein.…”

Convergence Result for Solving the Split Fixed Point Problem with Multiple Output Sets in Nonlinear Spaces

“…Byrne's CQ algorithm [2] is a popular technique for finding the solution of the SCFP. This algorithm has been extended for the multiple-sets split convex feasibility problem by many authors, like [1,14,15]. In the year 2020, Reich and Tuyen [13] introduced and examined the split feasibility problem with multiple output sets in Hilbert Spaces.…”