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Iterative processes with errors for nonlinear equations

Published online by Cambridge University Press:  17 April 2009

Łjubomir Ćirić  and
Jeong Sheok Ume
Łjubomir Ćirić
Affiliation:
Faculty of Mechanical Engineering, University of Blegrade, Belgrade, 27. marta 80, Yugoslavia e-mail: lciric@mas.bg.ac.yu
Jeong Sheok Ume
Affiliation:
Depatment of Applied Mathematics, Changwon National University, Changwon 641-773, Korea e-mail: jsume@changwon.ac.kr
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In this paper we introduce and consider a class of multi-valued and single-valued operators of generalised monotone type. We proved a new general lemma on the convergence of real sequences and some new convergence theorems for the Ishikawa and Mann iteration processes with errors to the unique fixed point of such operators, which are not necessarily Lipschitz operators. Our results generalise, improve, and extend several recent results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 177 - 189
Copyright
Copyright © Australian Mathematical Society 2004

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