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Convergence theorems for Bregman strongly nonexpansive mappings in reflexive Banach spaces. (English) Zbl 1466.47049

Summary: In this paper, we study a strong convergence theorem for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. As a consequence, we prove a convergence theorem to a common fixed point of a finite family of Bergman relatively nonexpansive mappings. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common zero of a finite family of Bregman inverse strongly monotone mappings and a solution of a finite family of variational inequality problems.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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