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Random approximation with weak contraction random operators and a random fixed point theorem for nonexpansive random self-mappings

Research paper by Suhong Li, Xin Xiao, Lihua Li, Jinfeng Lv

Indexed on: 19 Jan '12Published on: 19 Jan '12Published in: Journal of Inequalities and Applications



Abstract

In real reflexive separable Banach space which admits a weakly sequentially continuous duality mapping, the sufficient and necessary conditions that nonexpansive random self-mapping has a random fixed point are obtained. By introducing a random iteration process with weak contraction random operator, we obtain a convergence theorem of the random iteration process to a random fixed point for nonexpansive random self-mappings.