Fixed point of asymptotic pointwise nonexpansive semigroups in metric spaces

Saleh Abdullah Al-Mezel; Mohamed Amine Khamsi

doi:10.1186/1687-1812-2013-230

Fixed point of asymptotic pointwise nonexpansive semigroups in metric spaces

Saleh Abdullah Al-Mezel^*, Mohamed Amine Khamsi

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

Abstract

Let C be a bounded, closed, convex subset of a uniformly convex metric space (M, d). In this paper, we introduce the concept of asymptotic pointwise nonexpansive semigroups of nonlinear mappings T_t: C → C , i.e., a family such that T₀ (x ) = x, T_s+t = T_s (T_t (x )), and d (T_t (x), T_t (y )) ≤ α_t (x)d(x , y ), where lim sup_{t →∞} α_t (x) ≤ 1 for every x ∈ C . Then we investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups. The proof is based on the concept of types extended to one parameter family of points.

Original language	English
Article number	230
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2013
DOIs	https://doi.org/10.1186/1687-1812-2013-230
State	Published - Aug 2013

Keywords

Fixed point
Hyperbolic metric space
Inequality
Mann process
Nearest point projection
Nonexpansive mapping
Semigroup
Uniformly convex metric space
Uniformly lipschitzian mapping

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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Cite this

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title = "Fixed point of asymptotic pointwise nonexpansive semigroups in metric spaces",

abstract = "Let C be a bounded, closed, convex subset of a uniformly convex metric space (M, d). In this paper, we introduce the concept of asymptotic pointwise nonexpansive semigroups of nonlinear mappings Tt: C → C , i.e., a family such that T0 (x ) = x, Ts+t = Ts (Tt (x )), and d (Tt (x), Tt (y )) ≤ αt (x)d(x , y ), where lim supt →∞ αt (x) ≤ 1 for every x ∈ C . Then we investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups. The proof is based on the concept of types extended to one parameter family of points.",

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journal = "Fixed Point Theory and Algorithms for Sciences and Engineering",

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T1 - Fixed point of asymptotic pointwise nonexpansive semigroups in metric spaces

AU - Al-Mezel, Saleh Abdullah

AU - Khamsi, Mohamed Amine

PY - 2013/8

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N2 - Let C be a bounded, closed, convex subset of a uniformly convex metric space (M, d). In this paper, we introduce the concept of asymptotic pointwise nonexpansive semigroups of nonlinear mappings Tt: C → C , i.e., a family such that T0 (x ) = x, Ts+t = Ts (Tt (x )), and d (Tt (x), Tt (y )) ≤ αt (x)d(x , y ), where lim supt →∞ αt (x) ≤ 1 for every x ∈ C . Then we investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups. The proof is based on the concept of types extended to one parameter family of points.

AB - Let C be a bounded, closed, convex subset of a uniformly convex metric space (M, d). In this paper, we introduce the concept of asymptotic pointwise nonexpansive semigroups of nonlinear mappings Tt: C → C , i.e., a family such that T0 (x ) = x, Ts+t = Ts (Tt (x )), and d (Tt (x), Tt (y )) ≤ αt (x)d(x , y ), where lim supt →∞ αt (x) ≤ 1 for every x ∈ C . Then we investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups. The proof is based on the concept of types extended to one parameter family of points.

KW - Fixed point

KW - Hyperbolic metric space

KW - Inequality

KW - Mann process

KW - Nearest point projection

KW - Nonexpansive mapping

KW - Semigroup

KW - Uniformly convex metric space

KW - Uniformly lipschitzian mapping

UR - https://www.scopus.com/pages/publications/84902578731

U2 - 10.1186/1687-1812-2013-230

DO - 10.1186/1687-1812-2013-230

M3 - Article

AN - SCOPUS:84902578731

SN - 1687-1820

VL - 2013

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

M1 - 230

ER -

Fixed point of asymptotic pointwise nonexpansive semigroups in metric spaces

Abstract

Keywords

ASJC Scopus subject areas

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