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Common fixed points of two nonexpansive mappings in Banach spaces

Published online by Cambridge University Press:  17 April 2009

Tomonari Suzuki
Tomonari Suzuki
Affiliation:
Department of Mathematics and Information Science, Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan, e-mail: tomonari@math.sc.niigata-u.ac.jp
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In this paper, we discuss a necessary and sufficient condition for common fixed points of two nonexpansive mappings. We then prove a convergence theorem to a common fixed point. Finally, we discuss the existence of a nonexpansive retraction onto the set of common fixed points of nonexpansive mappings. In these theorems, we do not assume the strict (uniform) convexity of the norm of the Banach space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 1 - 18
Copyright
Copyright © Australian Mathematical Society 2004

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