location:  Publications → journals → CMB
Abstract view

# Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces

Published:2014-05-07
Printed: Jun 2015
• M. A. Khamsi,
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
 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
 MSC Classifications: 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