[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2003.18.2.251

NECESSARY AND SUFFICIENT CONDITIONS FOR CONVERGENCE OF ISHIKAWA ITERATIVE SCHEMES WITH ERRORS TO φ-HEMICONTRACTIVE MAPPINGS

Liu, Seqing (Department of Mathematics Liaoning Normal University)
Kim, Jong-Kyu (Department of Mathematics Kyungnam University)
Kang, Shin-Min (Department of mathematics Gyeongsang National University)

Publication Information

Communications of the Korean Mathematical Society / v.18, no.2, 2003 , pp. 251-261 More about this Journal

Abstract

The purpose of this paper is to establish the necessary and sufficient conditions which ensure the strong convergence of the Ishikawa iterative schemes with errors to the unique fixed point of a $\Phi$ -hemicontractive mapping defined on a nonempty convex subset of a normed linear space. The results of this paper extend substantially most of the recent results.

Keywords

${\Phi}$ -hemicontractive mapping; strongly pseudocontractive mapping; ${\Phi}$ -strongly pseudocontractive mapping; strictly hemicontractive mapping; Ishikawa iterative scheme with errors;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	Iterative solutions of nonlinear equations in smooth Banach spaces / [ C.E.Chidume ] / Nonlinear Anal. T. M. A. DOI ScienceOn
2	Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations / [ Y.XU ] / J. Math. Anal. Appl. DOI ScienceOn
3	Convergence theorems for strictly psudo-contractive and strongly accretrive maps / [ C.E.Chidume ] / J. Math. Anal. Appl.
4	Fixed point by a new iteration method / [ S.Ishikawa ] / Proc. Amer. Math. Soc. DOI ScienceOn
5	Approximation of fixed points of a strictly psedocontractive mapping / [ L.W.Liu ] / Proc. Amer. Math. Soc. DOI ScienceOn
6	Ishikawa and Mann iterative process with errors for nonlinear storngly accretive mappings in Banach spaces / [ L.S.Liu ] / J. Math. Anal. Appl. DOI ScienceOn
7	Fixed point iterations for strictly hemicontractive maps in uniformly smooth Banach spaces / [ C.E.Chidume;M.O.Osilike ] / Numer. Funct. Anal. Optimiz. DOI
8	Ishikawa iteration process for onlinear Lipschitz strongly accretive mappings / [ C.E.Chidume;M.O.Osilike ] / J. Math. Anal. Appl. DOI ScienceOn
9	Approximation of fixed points of strongly pseudo-contractive mappings / [ C.E.Chidume ] / Proc. Amer. Math. Soc. DOI ScienceOn
10	Iterative approaximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces / [ S.S.Chang;Y.J.Cho;B.S.Lee;S.M.Kang ] / J. Math. Anal. appl. DOI ScienceOn
11	Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces / [ K.K.Tan;H.K.Xu ] / J. Math. Anal. Appl. DOI ScienceOn
12	Fixed point iterations for certain classes of nonlinear mappings / [ C.E.Chidume ] / Applicable Anal. DOI ScienceOn
13	Nonlinear semigroups and evolution equations / [ T.Kato ] / J. Math. Soc. Japan DOI
14	Mean value methods in iteration / [ W.R.Mann ] / Proc. Amer. Math. Soc.
15	Iterative solution of nonlinear equations of Ø-storngly accretive type / [ M.O.osilike ] / J. Math. Anal. Appl. DOI ScienceOn
16	Ishikawa and Mann iterative processes with errors for nonlinear <TEX>$\phi$</TEX>-strongly quasi-accretive mappings in normed linear spaces / [ H.Y.zhou;Y.J.Cho ] / J. Korean Math. Soc. 과학기술학회마을
17	Iterative solutions of nonlinear equations with strongly accretive operators / [ C.E.Chidume ] / J. Math. Anal. Appl. DOI ScienceOn
18	Some problems and results in the study of nonlinear analysis / [ S.S.Chang ] / Nonlinear Anal. DOI ScienceOn
19	On a theorem of C. E. Chidume concerning the iterative approximaton of fixed points / [ J.Schu ] / Math. Nachr. DOI
20	Iterative solution of nonlinear accretive operator equations in arbitrary Banach spaces / [ C.E.Chidume;M.O.Osilike ] / Nonlinear Anal. DOI ScienceOn
21	Iterative approaximation of fixed point of Lipschitz strictly pseu-doccontractive mappings / [ C.E.Chidume ] / Proc. Amer. Math. Soc. DOI ScienceOn