CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces

  • M. A. Khamsi,
    Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   LaTeX   MathJax   PDF  

Abstract

In this paper, we investigate the common approximate fixed point sequences of nonexpansive semigroups of nonlinear mappings $\{T_t\}_{t \geq 0}$, i.e., a family such that $T_0(x)=x$, $T_{s+t}=T_s(T_t(x))$, where the domain is a metric space $(M,d)$. In particular we prove that under suitable conditions, the common approximate fixed point sequences set is the same as the common approximate fixed point sequences set of two mappings from the family. Then we use the Ishikawa iteration to construct a common approximate fixed point sequence of nonexpansive semigroups of nonlinear mappings.
Keywords: approximate fixed point, fixed point, hyperbolic metric space, Ishikawa iterations, nonexpansive mapping, semigroup of mappings, uniformly convex hyperbolic space approximate fixed point, fixed point, hyperbolic metric space, Ishikawa iterations, nonexpansive mapping, semigroup of mappings, uniformly convex hyperbolic space
MSC Classifications: 47H09, 46B20, 47H10, 47E10 show english descriptions Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
Geometry and structure of normed linear spaces
Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]
unknown classification 47E10
47H09 - Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
46B20 - Geometry and structure of normed linear spaces
47H10 - Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]
47E10 - unknown classification 47E10
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/