## Abstract and Applied Analysis

### Strong Convergence Theorems for Asymptotically Weak $G$-Pseudo-$\mathrm{\Psi }$-Contractive Non-Self-Mappings with the Generalized Projection in Banach Spaces

Yuanheng Wang

#### Abstract

A new concept of the asymptotically weak $G$-pseudo-$\mathrm{\Psi }$-contractive non-self-mapping $T:G{\mapsto}B$ is introduced and some strong convergence theorems for the mapping are proved by using the generalized projection method combined with the modified successive approximation method or with the modified Mann iterative sequence method in a uniformly and smooth Banach space. The proof methods are also different from some past common methods.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 651304, 11 pages.

Dates
First available in Project Euclid: 28 March 2013

https://projecteuclid.org/euclid.aaa/1364475917

Digital Object Identifier
doi:10.1155/2012/651304

Mathematical Reviews number (MathSciNet)
MR2994942

#### Citation

Wang, Yuanheng. Strong Convergence Theorems for Asymptotically Weak $G$ -Pseudo- $\mathrm{\Psi }$ -Contractive Non-Self-Mappings with the Generalized Projection in Banach Spaces. Abstr. Appl. Anal. 2012 (2012), Article ID 651304, 11 pages. doi:10.1155/2012/651304. https://projecteuclid.org/euclid.aaa/1364475917

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