The equivalence of Mann and Ishikawa iteration for a Lipschitzian ψ-uniformly pseudocontractive and ψ-uniformly accretive maps

Abstract

We consider a mean value iteration for a family of functions, which corresponds to the Mann iteration with \(\lim_{n\rightarrow \infty}an\neq0\). We prove convergence results for this iteration when applied to strongly pseudocontractive or strongly accretive maps.

Authors

B. E. Rhoades
Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, U.S.A
S.M. Soltuz
Tiberiu Popoviciu Institute of Numerical Analysis

Keywords

Mann iteration, Ishikawa iteration, ψuniformly pseudocontractive, ψ uniformly accretive map.

Paper coordinates

B.E. Rhoades and Ş.M. Şoltuz, The equivalence of Mann and Ishikawa iteration for a Lipschitzian ψ-uniformly pseudocontractive and ψ-uniformly accretive map, Tamkang J. Math. , vol. 35, no.3,  (2004), pp. 235-245, https://doi.org/10.5556/j.tkjm.35.2004.204

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About this paper

Journal

Tamkang Journal of Mathematics

Publisher Name

Tamkang University, Tamsui, Taiwan, R.O.C.

DOI
Print ISSN

0049-2930

 

Online ISSN

2073-9826

google scholar link

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