On the convergence between the Mann iteration and Ishikawa iteration for the generalized Lipschitzian and $\Phi$-strongly pseudocontractive mappings
Bull. Korean Math. Soc. 2008 Vol. 45, No. 4, 635-644
Printed December 1, 2008
Zhiqun Xue
Shijiazhuang Railway Institute
Abstract : In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and $\Phi$-strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. $\bf 42$ (2003), 2645--2651].
Keywords : Ishikawa iteration, Mann iteration, $\Phi$-strongly pseudocontractive maps, generalized Lipschitz maps, uniformly smooth Banach spaces
MSC numbers : 47H09, 47H10, 47H17
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