IJPAM: Volume 94, No. 1 (2014)

COMMON FIXED POINT THEOREMS FOR
A ĆIRIĆ-REICH-RUS PAIR OF MAPPINGS
IN METRIC SPACES WITH A DIRECTED GRAPH

Narongsuk Boonsri$^1$, Somchit Chotchaisthit$^2$, Satit Saejung$^3$
$^{1,2}$Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen, 40002, THAILAND
$^{2,3}$The Centre of Excellence in Mathematics
Commission on Higher Education (CHE)
Sri Ayudthaya Road, Bangkok, 10400, THAILAND


Abstract. Let $(X,d)$ be a complete metric space with a directed graph $G$. Inspired by the work of Bojor, we introduce a new contractive type condition between a pair of mappings $S,T : X \to X$ with respect to $G$. In particular, if $S=T$, we obtain the result of Bojor. Moreover, we also establish a result under an independent hypothesis.

An example showing that it is applicable in our setting but not in Bojor's is given.

Received: October 21, 2013

AMS Subject Classification: 47H10, 54H25, 55M20

Key Words and Phrases: fixed point, Ćirić-Reich-Rus mapping, metric space with a directed graph

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DOI: 10.12732/ijpam.v94i1.5 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 94
Issue: 1
Pages: 45 - 53

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).