Generalized equilibrium and fixed point problems for Bregman relatively nonexpansive mappings in Banach spaces. (English) Zbl 1401.47006
Summary: In this paper, we introduce and study a hybrid iterative method for finding a common solution of a generalized equilibrium problem and a fixed point problem for a Bregman relatively nonexpansive mapping in reflexive Banach spaces. We prove that the sequences generated by the hybrid iterative algorithm converge strongly to a common solution of these problems. Further, we give some consequences of the main result. Finally, we discuss a numerical example to demonstrate the applicability of the iterative algorithm.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H05 | Monotone operators and generalizations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
generalized equilibrium problem; Bregman relatively nonexpansive mapping; hybrid iterative method; strong convergenceReferences:
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