Approximation of common solutions for a fixed point problem of asymptotically nonexpansive mapping and a generalized equilibrium problem in Hilbert space

Authors

Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania

https://doi.org/10.1186/s42787-019-0051-8

Abstract

In this paper, we introduce an iterative algorithm to approximate a common solution
of a generalized equilibrium problem and a fixed point problem for an asymptotically
nonexpansive mapping in a real Hilbert space. We prove that the sequences generated
by the iterative algorithm converge strongly to a common solution of the generalized
equilibrium problem and the fixed point problem for an asymptotically nonexpansive
mapping. The results presented in this paper extend and generalize many previously
known results in this research area. Some applications of main results are also provided.

Keywords

Journal of the Egyptian Mathematical Society
Volume 27, Issue 1
2019
Pages 1-16

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