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http://dx.doi.org/10.4134/BKMS.2010.47.2.295

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

Xue, Zhiqun (DEPARTMENT OF MATHEMATICS AND PHYSICS SHIJIAZHUANG RAILWAY INSTITUTE)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.2, 2010 , pp. 295-305 More about this Journal
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;
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