Halpern-Mann’s iterations for Bregman strongly nonexpansive mappings in reflexive Banach spaces with applications. (English) Zbl 1279.47091
Summary: We investigate strong convergence for Bregman strongly nonexpansive mappings by modifying Halpern and Mann’s iterations in the framework of a reflexive Banach space. As applications, we apply our main result to problems of finding zeros of maximal monotone operators and equilibrium problems in reflexive Banach spaces.
MSC:
47J25 | Iterative procedures involving nonlinear operators |
47H05 | Monotone operators and generalizations |
47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
Bregman strongly nonexpansive mapping; Bregman projection; Legendre function; totally convex function; Halpern’s iteration; Mann’s iterationReferences:
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