Convergence theorem for zeros of generalized Lipschitz generalized phi-quasi-accretive operators

Authors:
C. E. Chidume and C. O. Chidume

Journal:
Proc. Amer. Math. Soc. **134** (2006), 243-251

MSC (2000):
Primary 47H09, 47J25

DOI:
https://doi.org/10.1090/S0002-9939-05-07954-2

Published electronically:
June 13, 2005

MathSciNet review:
2170564

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a uniformly smooth real Banach space and let be a mapping with . Suppose is a generalized Lipschitz generalized -quasi-accretive mapping. Let and be real sequences in [0,1] satisfying the following conditions: (i) ; (ii) ; (iii) ; (iv) Let be generated iteratively from arbitrary by

where is defined by and is an arbitrary bounded sequence in . Then, there exists such that if the sequence converges strongly to the unique solution of the equation . A related result deals with approximation of the unique fixed point of a generalized Lipschitz and generalized -hemi-contractive mapping.

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Additional Information

**C. E. Chidume**

Affiliation:
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Email:
chidume@ictp.trieste.it

**C. O. Chidume**

Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, Alabama

Email:
chidumeg@hotmail.com

DOI:
https://doi.org/10.1090/S0002-9939-05-07954-2

Keywords:
Generalized Lipschitz maps,
generalized $\Phi$-quasi-accretive maps,
generalized $\Phi$-hemicontractive maps,
uniformly smooth real Banach spaces

Received by editor(s):
August 2, 2004

Received by editor(s) in revised form:
August 30, 2004

Published electronically:
June 13, 2005

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2005
American Mathematical Society