Convergence theorems and stability results of pointwise asymptotically nonexpansive mapping in Banach space

Volume 10, Issue 10, pp 5165--5173

Publication Date: 2017-10-12

http://dx.doi.org/10.22436/jnsa.010.10.04

Authors

Qiansheng Feng - Department of Mathematics, Tianjin University, Tianjin, 300354, China
Nan Jiang - Department of Mathematics, Tianjin University, Tianjin, 300354, China
Yongfu Su - Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China

Abstract

The purpose of this paper is to approximate the fixed point of pointwise asymptotically nonexpansive mapping using the generalized Mann and generalized Ishikawa iterative scheme. And under the condition that the pointwise asymptotically nonexpansive mapping is compact, the stability results of the two iterative schemes are studied. The main results of this paper modify and improve many important recent results in the literature.

Keywords

Pointwise asymptotically nonexpansive mapping, generalized Mann iterative scheme, generalized Ishikawa iterative scheme, stability result, convergence theorem

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