# IJPAM: Volume 75, No. 2 (2012)

**SOME COMMON FIXED POINT THEOREMS OF**

MULTIVALUED MAPPINGS AND FUZZY

MAPPINGS IN ORDERED METRIC SPACES

MULTIVALUED MAPPINGS AND FUZZY

MAPPINGS IN ORDERED METRIC SPACES

Department of Mathematics

University of Texas - Pan American

Edinburg, Texas, 78539, USA

**Abstract. **Heilpern [9] introduced the concept of fuzzy
mappings and proved a fixed point theorem for fuzzy contraction mappings.
Generalizing Heilpern's result, Bose and Sahani [5] proved a common
fixed point theorem for a pair of generalized fuzzy contraction mappings
and also a fixed point theorem for nonexpansive fuzzy mappings. Since
then, many authors have generalized Bose and Sahani's results in different
directions. Also Bose and mukherjee (see [2], [3]) considered common
fixed points of a pair of multivalued mappings and a sequence of single
valued mappings. We present several theorems which are generalized
to ordered metric space setting.In Section 3, we present our remarks
concerning some generalizations of the main theorm of Bose and Sahani.Three
such results, of Vijayaraju and Marudai [18], Azam and Arshad
[1], and B.S. Lee et al [13] are discussed and a correct proof
of the main theorem of Vijayaraju and Marudai has ben presented using
a tecnique of Bose and Mukherjee [2]. In Section 4, we present
several new theorems in ordered metric space setting. One is a version
of the fixed point theorem for a pair of multivalued mappings of Bose
and Mukherjee in ordered metric space setting and the other is a new
version of the main theorem of Bose and Sahani in orderd metric space
setting. Also we present a few results concerning common fixed point
of a sequence of such mappings in ordered metric space setting.

**Received: **July 8, 2011

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

**Key Words and Phrases: **common fixed points, fuzzy mappings, fuzzy fixed points, ordered metric spaces

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

**ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2012

**Volume:**75

**Issue:**2