The convergence theorems for common fixed points of uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings
Bull. Korean Math. Soc. 2010 Vol. 47, No. 2, 295-305
https://doi.org/10.4134/BKMS.2010.47.2.295
Printed March 1, 2010
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
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