Viscosity approximation methods for pseudo-contractive semigroups in Banach spaces

Xue Song Li; Nan Jing Huang; Donal O'Regan

doi:10.1016/j.na.2012.01.031

Viscosity approximation methods for pseudo-contractive semigroups in Banach spaces

Xue Song Li
, Nan Jing Huang
, Donal O'Regan

Mathematics

Sichuan University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

3 Citations (Scopus)

Abstract

We study the strong convergence of two viscosity iteration processes for pseudo-contractive semigroup and for φ-strongly pseudo-contractive mapping in uniformly convex Banach spaces with uniformly Gteaux differentiable norm. As special cases, we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain Banach spaces. The results presented in this paper extend and generalize previous results.

Original language	English
Pages (from-to)	3776-3786
Number of pages	11
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	75
Issue number	9
DOIs	https://doi.org/10.1016/j.na.2012.01.031
Publication status	Published - Jun 2012

Keywords

Common fixed point
Nonexpansive semigroup
Pseudo-contractive semigroup
Viscosity approximation
φ-strongly pseudo-contractive mapping

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10.1016/j.na.2012.01.031

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abstract = "We study the strong convergence of two viscosity iteration processes for pseudo-contractive semigroup and for φ-strongly pseudo-contractive mapping in uniformly convex Banach spaces with uniformly Gteaux differentiable norm. As special cases, we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain Banach spaces. The results presented in this paper extend and generalize previous results.",

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AB - We study the strong convergence of two viscosity iteration processes for pseudo-contractive semigroup and for φ-strongly pseudo-contractive mapping in uniformly convex Banach spaces with uniformly Gteaux differentiable norm. As special cases, we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain Banach spaces. The results presented in this paper extend and generalize previous results.

KW - Common fixed point

KW - Nonexpansive semigroup

KW - Pseudo-contractive semigroup

KW - Viscosity approximation

KW - φ-strongly pseudo-contractive mapping

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DO - 10.1016/j.na.2012.01.031

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 9

ER -

Viscosity approximation methods for pseudo-contractive semigroups in Banach spaces

Abstract

Keywords

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