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http://dx.doi.org/10.4134/BKMS.2008.45.4.635

ON THE ON THE CONVERGENCE BETWEEN THE MANN ITERATION AND ISHIKAWA ITERATION FOR THE GENERALIZED LIPSCHITZIAN AND Φ-STRONGLY PSEUDOCONTRACTIVE MAPPINGS

Xue, Zhiqun (DEPARTMENT OF MATHEMATICS AND PHYSICS SHIJIAZHUANG RAILWAY INSTITUTE)

Publication Information

Bulletin of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 635-644 More about this Journal

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. 42 (2003), 2645.2651].

Keywords

Ishikawa iteration; Mann iteration; $\Phi$ -strongly pseudocontractive maps; generalized Lipschitz maps; uniformly smooth Banach spaces;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)
Times Cited By SCOPUS : 1

Reference
Cited By SCOPUS

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