Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces

Authors

Shanguang Qian - Architectural Engineering Faculty, Kunming Metallurgy College, Kunming, Yunnan, P. R. China.
Wei-Qi Deng - School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, P. R. China.

Abstract

Based on a specific way of choosing the indices and a new concept, namely, an analogue of inner product, a modified Krasnoselski-Mann iteration scheme is proposed for approximating common fixed points of a countable family of asymptotically nonexpansive mappings; and a strong convergence theorem is established in the framework of CAT(0) spaces. Our results greatly improve and extend those of the authors whose related researches just involve a single mapping and the weaker \(\Delta\)-convergence.

Keywords

Krasnoselski-Mann iteration, CAT(0) spaces, infinite families of nonexpansive mappings, strong convergence, \(\Delta\)-convergence.

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