IJPAM: Volume 18, No. 1 (2005)

THE EQUIVALENCE AMONG MODIFIED MANN
ITERATION, MODIFIED ISHIKAWA ITERATION
AND MODIFIED MULTISTEP ITERATION

Zeqing Liu$^1$, Beibei Zhu$^2$, Shin Min Kang$^3$, Sang Keun Lee$^4$
$^{1,2}$Department of Mathematics
Liaoning Normal University
P.O. Box 200, Dalian, Liaoning, 116029, P.R. CHINA
$^1$e-mail: zeqingliu@dl.cn
$^{3,4}$Department of Mathematics
Research Institute of Natural Science
Gyeongsang National University
Chinju, 660-701, KOREA
$^3$e-mail: smkang@nongae.gsnu.ac.kr


Abstract.The purpose of this paper is to investigate the convergence of modified Mann iteration and modified Ishikawa iteration are equivalent to the convergence of modified multistep iteration which is introduced by Rhoades and Soltuz in Nonlinear Anal., 58 (2004), 219-228, for some kinds of nonlinear mappings. Furthermore, we show that the equivalence of stability among modified Mann iteration, modified Ishikawa iteration and modified multistep iteration.

Received: September 12, 2004

AMS Subject Classification: 47H10

Key Words and Phrases: modified Mann iteration, modified Ishikawa iteration, modified multistep iteration, asymptotically nonexpansive mapping in the intermediate sense, strongly successively pseudocontractive mapping

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 1