Volume 29, Issue 1
More on Fixed Point Theorem of {a,b,c}-Generalized Nonexpansive Mappings in Normed Spaces

S. M. Ali

10.4208/ata.2013.v29.n1.1

Anal. Theory Appl., 29 (2013), pp. 1-11

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  • 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 contractingpoint and $T$ be an $\{a,b,c\}$-generalized-nonexpansive mapping from $C$ into $C$. We prove that the infimum of the set $\{\| x-T(x) \|\}$ 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.

  • History

Published online: 2013-03

  • AMS Subject Headings

42B25, 42B20

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