Strong convergence of hybrid Halpern processes in a Banach space

Volume 9, Issue 4, pp 1776--1786 http://dx.doi.org/10.22436/jnsa.009.04.33

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Authors

Yuan Hecai - School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Henan, China. Zhaocui Min - School of Science, Hebei University of Engineering, Hebei, China.

Abstract

The purpose of this paper is to investigate convergence of a hybrid Halpern process for fixed point and equilibrium problems. Strong convergence theorems of common solutions are established in a strictly convex and uniformly smooth Banach space which also has the Kadec-Klee property.

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Keywords

• Asymptotically nonexpansive mapping
• fixed point
• quasi-\(\phi\)-nonexpansive mapping
• equilibrium problem
• generalized projection.

MSC

•  65J15
•  90C30

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