Split common fixed point and common null point problem

Abstract

In this paper, we present a new algorithm for solving the split common null point and common fixed point problem, to find a point that belongs to the common element of common zero points of an infinite family of maximal monotone operators and common fixed points of an infinite family of demicontractive mappings such that its image under a linear transformation belongs to the common zero points of another infinite family of maximal monotone operators and its image under another linear transformation belongs to the common fixed point of another infinite family of demicontractive mappings in the image space. We establish strong convergence for the algorithm to find a unique solution of the variational inequality, which is the optimality condition for the minimization problem. As special cases, we shall use our results to study the split equilibrium problems and the split optimization problems. KEYWORDS common fixed point problem, maximal monotone operator, split common null point, split equilibrium problem, split optimization problems 7410

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]…”