THE CONVERGENCE THEOREMS FOR COMMON FIXED POINTS OF UNIFORMLY L-LIPSCHITZIAN ASYMPTOTICALLY Φ-PSEUDOCONTRACTIVE MAPPINGS

Title & Authors
THE CONVERGENCE THEOREMS FOR COMMON FIXED POINTS OF UNIFORMLY L-LIPSCHITZIAN ASYMPTOTICALLY Φ-PSEUDOCONTRACTIVE MAPPINGS
Xue, Zhiqun;

Abstract
In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically $\small{\Phi}$-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 $\small{\Phi}$-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 $\small{\Phi}$-pseudocontractive mapping;modified Mann iterative process;modified Ishikawa iterative process;fixed point;
Language
English
Cited by
1.
The equivalence between the convergence of the modified Mann and Ishikawa iterations for asymptotically pseudocontractive mappings obtained by dropping the bounded assumption, Journal of Inequalities and Applications, 2014, 2014, 1, 293
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