Vol. LXXVI, 1 (2007)
p. 285 - 298

Almost Stable Iteration Schemes for Local Strongly Pseudocontractive and Local Strongly Accretive Operators
in Real Uniformly Smooth Banach Spaces

Zeqing Liu, Yuguang Xu and Shin Min Kang

Received: July 4, 2007;   Revised: January 15, 2008;   Accepted: February 04, 2008

Abstract.   In this paper we establish the strong convergence and almost stability of the Ishikawa iteration methods with errors for the iterative approximations of either fixed points of local strongly pseudocontractive operators or solutions of nonlinear operator equations with local strongly accretive type in real uniformly smooth Banach spaces. Our convergence results extend some known results in the literature.

Keywords:  Local strongly accretive operator; local strongly pseudocontractive operator; Ishikawa iteration sequence with errors; fixed point; convergence; almost stability; nonempty bounded closed convex subset; real uniformly smooth Banach space  

AMS Subject classification: Primary:  47H06, 47H10, 47H15, 47H17

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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Comenius University
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