IJPAM: Volume 61, No. 1 (2010)
MAPPINGS AND FUZZY MAPPINGS



The University of Texas - Pan American
1201, West University Drive, Edinburg, TX 78539-2999, USA


Abstract.In this paper, a common fixed point theorem for a pair of
multi-valued mappings which satisfy a generalized -weakly
contractive condition in a complete metric space setting is proved.
A fixed point theorem is also proved when the mapping is a non-self
mapping with domain a nonempty closed subset of a complete and
convex metric space. A coincidence point theorem concerning a
single-valued mapping
and a pair of
-weakly contractive
multi-valued mappings with respect to
is also proved. Next two
theorems deal with fuzzy mappings in a metric linear space setting:
the first one is a common fixed point theorem for a pair of fuzzy
mappings, a fuzzy version of the result obtained for a pair of
multi-valued mappings, and the second one is a coincidence point
theorem concerning a
-weakly contractive fuzzy mapping with
respect to mapping
. These results extend the work of several
authors.
Received: March 27, 2010
AMS Subject Classification: 03E72, 47H04, 47H10, 54H25, 54C60
Key Words and Phrases: fixed point, multi-valued mapping, fuzzy mapping, weak contraction
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 1