Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(2): 295-305

Printed March 1, 2010

https://doi.org/10.4134/BKMS.2010.47.2.295

Copyright © The Korean Mathematical Society.

The convergence theorems for common fixed points of uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings

Zhiqun Xue

Shijiazhuang Railway Institute

Abstract

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Finally, we obtain the convergence theorems of Ishikawa iterative sequence and the modified Ishikawa iterative process with errors.

Keywords: uniformly L-Lipschitzian, asymptotically $\Phi$-pseudocontractive mapping, modified Mann iterative process, modified Ishikawa iterative process, fixed point

MSC numbers: 47H10 47H09 46B20