Implicit iterative algorithms of the split common fixed point problem for Bregman quasi-nonexpansive mapping in Banach spaces

Abstract

In this paper, we study a modified implicit rule for finding a solution of split common fixed point problem of a Bregman quasi-nonexpansive mapping in Banach spaces. We propose a new iterative algorithm and prove the strong convergence theorem under appropriate conditions. As an application, the results are applied to solving the zero problem and the equilibrium problem.

Key words： Split common fixed point; implicit rule; Bregman quasi-nonexpansive mapping; strong convergence; Banach space

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 12171435) and the Natural Science Foundation of Zhejiang Province (Grant No. LY14A010011).

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