Strong convergence theorems for the general split common fixed point problem in Hilbert spaces

Abstract

In this paper, we propose and investigate a new iterative algorithm for solving the general split common fixed point problem in the setting of infinite-dimensional Hilbert spaces. We also prove the sequence generated by the proposed algorithm converge strongly to a common solution of the general split common fixed point problem. As application, some particular cases of directed operator and quasi-nonexpansive operator are also considered. Finally, we present several numerical results for general split common fixed point problem to demonstrate the efficiency of the proposed algorithm. c 2017 All rights reserved.Keywords: General split common fixed point problem, demicontractive operator, quasi-nonexpansive operator, directed operator. 2010 MSC: 47J25, 47H09, 65J25.

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]…”