Strong convergence of a general iterative algorithm for asymptotically nonexpansive semigroups in Banach spaces

Volume 9, Issue 10, pp 5695--5711 http://dx.doi.org/10.22436/jnsa.009.10.15

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Authors

Lishan Liu - School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China. - Department of Mathematics and Statistics, Curtin University, WA6845, Perth, Australia. Chun Liu - School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China. Fang Wang - School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China. Yonghong Wu - Department of Mathematics and Statistics, Curtin University, WA6845, Perth, Australia.

Abstract

In this paper, we study a general iterative process strongly converging to a common fixed point of an asymptotically nonexpansive semigroup \(\{T(t) : t \in \mathbb{R }^+\}\) in the framework of reflexive and strictly convex spaces with a uniformly Gáteaux differentiable norm. The process also solves some variational inequalities. Our results generalize and extend many existing results in the research field.

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Keywords

• Asymptotically nonexpansive semigroups
• variational inequality
• strong convergence
• reflexive and strictly convex Banach spaces
• fixed point.

MSC

•  47H09
•  47H10
•  49J30

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