# IJPAM: Volume 61, No. 1 (2010)

**FIXED POINT THEOREMS FOR MULTI-VALUED**

MAPPINGS AND FUZZY MAPPINGS

MAPPINGS AND FUZZY MAPPINGS

Department of Mathematics

The University of Texas - Pan American

1201, West University Drive, Edinburg, TX 78539-2999, USA

e-mails: rkbose@utpa.edu, rkbose@hotmail.com

e-mail: roychowdhurymk@utpa.edu

**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