Monther Rashed Alfuraidan

Caristi Fixed Point Theorem in Metric Spaces with a Graph

We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.

Remarks on Caristi’s fixed point theorem in metric spaces with a graph

AbstractWe discuss some extensions of Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem where the assumptions in Caristi’s theorem can, a priori, be weakened. It extends some recent works on Caristi’s fixed point theorem for mappings defined on metric spaces with a graph. MSC:47H09, 46B20, 47H10, 47E10.

FIBONACCI–MANN ITERATION FOR MONOTONE ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

We extend the results of Schu [‘Iterative construction of fixed points of asymptotically nonexpansive mappings’, J. Math. Anal. Appl. 158 (1991), 407–413] to monotone asymptotically nonexpansive mappings by means of the Fibonacci–Mann iteration process

Topological aspects of weighted graphs with application to fixed point theory

\begin{eqnarray}x_{n+1}=t_{n}T^{f(n)}(x_{n})+(1-t_{n})x_{n},\quad n\in \mathbb{N},\end{eqnarray}

Mann iteration process for monotone nonexpansive mappings with a graph

where

Inverse graphs associated with finite groups

T

Chapter 7 – Metric Fixed Point Theory in Spaces with a Graph

is a monotone asymptotically nonexpansive self-mapping defined on a closed bounded and nonempty convex subset of a uniformly convex Banach space and

Bipartite Distance-Transitive Doubles with Primitive Halved of Diameter Two

\{f(n)\}