Approximation of common solutions for a fixed point problem of asymptotically nonexpansive mapping and a generalized equilibrium problem in Hilbert space | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 27, Issue 1, 2019, Pages 1-16 PDF (551.39 K) | ||
| DOI: 10.1186/s42787-019-0051-8 | ||
| Authors | ||
| Richard Osward; Santosh Kumar; Mengistu Goa Sangago | ||
| Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania | ||
| 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 | ||
| Fixed points; Generalized equilibrium problem; Asymptotically nonexpansive mapping; Iterative algorithm | ||
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