In this paper we introduce a new algorithm based on the viscosity iteration method for solving the split common fixed point problem of two infinite families of k-demicontractive mappings. We shall also study the split common null point problem, and the split equilibrium problem for this class of mappings. As an application, we obtain strong convergence theorems for the split monotone variational inclusion problem and the split variational inequality problem. Our results improve and extend the recent results of Cui and Wang [9], Takahashi [21], Tang and Lui [22], Moudafi [15], Eslamian and Vahidi [17], and many others.
In this paper, we introduce a new algorithm for solving the split equality common null point problem and the equality fixed point problem for an infinite family of Bregman quasi-nonexpansive mappings in reflexive Banach spaces. We then apply this algorithm to the equality equilibrium problem and the split equality optimization problem. In this way, we improve and generalize the results of Takahashi and Yao [22], Byrne et al [9], Dong et al [11], and Sitthithakerngkiet et al [21].
Abstract:In this paper, we introduce an iterative algorithm for solving the split common fixed point problem for a family of multi-valued quasinonexpansive mappings and totally asymptotically strictly pseudocontractive mappings, as well as for a family of totally quasi-φ-asymptotically nonexpansive mappings and k-quasi-strictly pseudocontractive mappings in the setting of Banach spaces. Our results improve and extend the results of Tang et al., Takahashi, Moudafi, Censor et al., and Byrne et al.
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