Abstract
Let be a semitopological semigroup, a nonempty subset of a real Hilbert space , and a representation of as asymptotically nonexpansive type mappings of into itself. Let for each and . In this paper, we prove that is nonempty for each if and only if there exists a unique nonexpansive retraction of into such that for all and for every . Moreover, we prove the ergodic convergence theorem for a semitopological semigroup of non-Lipschitzian mappings without convexity.
Citation
G. Li. J. K. Kim. "Nonlinear ergodic theorems for a semitopological semigroup of non-Lipschitzian mappings without convexity." Abstr. Appl. Anal. 4 (1) 49 - 59, 1999. https://doi.org/10.1155/S1085337599000056
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