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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strong convergence results for nonself multimaps in Banach spaces


Authors: N. Shahzad and H. Zegeye
Journal: Proc. Amer. Math. Soc. 136 (2008), 539-548
MSC (2000): Primary 47H10, 47H09
Published electronically: November 3, 2007
MathSciNet review: 2358494
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Abstract: We prove strong convergence theorems for multimaps under mild conditions, which include Browder's convergence theorem as well as Reich's convergence theorem. We thus provide a partial answer to Jung's question.


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Additional Information

N. Shahzad
Affiliation: Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Email: nshahzad@kau.edu.sa

H. Zegeye
Affiliation: Bahir Dar University, P.O. Box. 859, Bahir Dar, Ethiopia
Email: habtuzh@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08884-3
PII: S 0002-9939(07)08884-3
Keywords: Nonexpansive multimap, fixed point, nonexpansive retract, Banach limit, inwardness, Banach space
Received by editor(s): June 21, 2006
Received by editor(s) in revised form: August 25, 2006
Published electronically: November 3, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society