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

被引：0

作者：

Richard Osward

Santosh Kumar

Mengistu Goa Sangago

机构：

[1] University of Dar es Salaam,Department of Mathematics, College of Natural and Applied Sciences

[2] Addis Ababa University,Department of Mathematics, College of Natural and Computational Science

来源：

Journal of the Egyptian Mathematical Society | / 27卷 / 1期

关键词：

Fixed points; Generalized equilibrium problem; Asymptotically nonexpansive mapping; Iterative algorithm; 47J05; 47J20; 47H09;

D O I：

10.1186/s42787-019-0051-8

中图分类号：

学科分类号：

摘要：

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.

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