Strong Convergence Theorems for Iterative Schemes with Errors for Asymptotically Demicontractive Mappings in Arbitrary Real Normed Linear Spaces

Volume 3, Issue 5, 2002

Article 83

STRONG CONVERGENCE THEOREMS FOR ITERATIVE SCHEMES WITH ERRORS FOR ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS IN ARBITRARY REAL NORMED LINEAR SPACES

YEOL JE CHO(1), HAIYUN ZHOU(2) AND SHIN MIN KANG(1)

⁽¹⁾DEPARTMENT OF MATHEMATICS,
GYEONGSANG NATIONAL UNIVERSITY,
CHINJU 660-701, KOREA
E-Mail: yjcho@nongae.gsnu.ac.kr

⁽²⁾DEPARTMENT OF MATHEMATICS,
SHIJIAZHUANG MECHANICAL ENGINEERING COLLEGE,
SHIJIAZHUANG 050003,
PEOPLE'S REPUBLIC OF CHINA.
E-Mail: luyao_846@163.com

Received 30 April, 2002; Accepted 5 September, 2002.
Communicated by: S.S. Dragomir

ABSTRACT. In the present paper, by virtue of new analysis technique, we have established several strong convergence theorems for the modified Ishikawa and Mann iteration schemes with errors for a class of asymptotically demicontractive mappings in arbitrary real normed linear spaces. Our results extend, generalize and improve the corresponding results obtained by Igbokwe [1], Liu [2], Osilike [3] and and others.

[1] D.I. IGBOKWE, Approximation of fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, to appear in J.Ineq. Pure and Appl. Math.
[2] Q.H. LIU, Convergence theorems of sequence of iterates for asymptotically demicontractive and hemicontractive mappings, Nonlinear Anal. Appl., 26 (1996), 1835--1842.
[3] M.O. OSILIKE, Iterative approximations of fixed points asymptotically demicontractive mappings, Indian J. Pure Appl. Math., 29 (1998), 1291--1300.

Key words:
Asymptotically demicontractive mapping, Modified Mann and Ishikawa iteration schemes with errors, Arbitrary linear space.

2000 Mathematics Subject Classification:
47H05, 47H10.

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