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More on Fixed Point Theorem of {a,b,c}-Generalized Nonexpansive Mappings in Normed Spaces

More on Fixed Point Theorem of $\{a,b,c\}$-Generalized Nonexpansive Mappings in Normed Spaces

Year:    2013

Analysis in Theory and Applications, Vol. 29 (2013), Iss. 1 : pp. 1–11

Abstract

Let X be a weakly Cauchy normed space in which the parallelogram law holds, C be a bounded closed convex subset of X with one contracting point and T be an {a,b,c}-generalized-nonexpansive mapping from C into C. We prove that the infimum of the set { on C is zero, study some facts concerning the \{a,b,c\}-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to C is singleton. Depending on the fact that the \{a,b,0\}-generalized-nonexpansive mapping from C into C has fixed points, accordingly, another version of the Browder's strong convergence theorem for mappings is given.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2013.v29.n1.1

Analysis in Theory and Applications, Vol. 29 (2013), Iss. 1 : pp. 1–11

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Fixed point theorem $\{a b c\}$-generalized-nonexpansive mapping asymptotic center Browder's strong convergence Theorem.