# IJPAM: Volume 56, No. 2 (2009)

**SOME COMMON FIXED POINT THEOREMS**

FOR FUZZY MAPPINGS

FOR FUZZY MAPPINGS

Department of Mathematics

The University of Texas - Pan American

Edinburg, Texas, 78539, USA

e-mail: rkbose@hotmail.com

**Abstract.**Zadeh [22] introduced the concept of
fuzzy sets and Heilpern [11] introduced the concept of fuzzy mappings.
Since then both the concepts have been generalized by various researchers.
Bose and Sahani [10] and others generalized the results of Heilpern.
Many authors considered class of fuzzy sets with nonempty compact
(convex) cut sets in a metric (linear) space, but some
have given attention to class of fuzzy sets with nonempty closed and
bounded cut sets in a metric space. Dong Qui and Lan Shu
[15] considered
(the class of fuzzy
sets with nonempty closed and bounded cut sets) equipped
with the generalized Hausdorff metric. They proved some common fixed
point theorems for fuzzy mappings
satisfying certain inequalities. Dong Qui et al [16] considered
the class of fuzzy sets, with nonempty compact cut sets
(
) and fuzzy mappings
.
This paper deals with several common fixed point theorems of such
fuzzy mappings satisfying various (different) inequalities and these
extend the works of various researchers. Following Alber and Guerre-Delabriere
[2], we extend the concept of weakly contractive condition
to the fuzzy mappings and prove a common fixed point theorem for a
pair of such fuzzy mappings. Also we prove a fixed point theorem for
a fuzzy mapping which is a
weak contraction
(introduced by Berinde and Berinde [6]).

**Received: **August 18, 2009

**AMS Subject Classification: **47H10, 03E72, 54H25

**Key Words and Phrases: **common fixed point, fuzzy mappings, weakly contractive
mappings,
weak contraction, contraction

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2009

**Volume:** 56

**Issue:** 2