Approximation to fixed points of generalized nonexpansive mappings

Wong, Chi Song

doi:10.1090/S0002-9939-1976-0390850-9

Approximation to fixed points of generalized nonexpansive mappings
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Proc. Amer. Math. Soc. 54 (1976), 93-97 Request permission

Abstract:

Let $K$ be a convex subset of a uniformly convex Banach space. It is proved that if $K$ is compact, then the fixed points of a continuous generalized nonexpansive self-mapping $T$ on $K$ can be approximated by the iterates of ${T_t}$ with $t \in (0,1),{T_t}(x) = (1 - t)x + tT(x),x \in K;{T_t}$ is asymptotically regular if $T$ has a fixed point.

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Common fixed points for two mappings

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Additional Information

Journal: Proc. Amer. Math. Soc. 54 (1976), 93-97
DOI: https://doi.org/10.1090/S0002-9939-1976-0390850-9
MathSciNet review: 0390850