Common fixed point theorems for new contraction without continuity completeness and compatibility property in partially ordered Fuzzy metric spaces
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After the inspirational innovation of fuzzy set by Zadeh in 1965, Kramosil and Michalek in 1975 pioneered the concept of fuzziness in metric spaces and very rst they formulated the notion of fuzzy met- ric spaces. Jungck introduced the idea of commutativity (in 1976) and compatibility (1986) in metric spaces and same are utilized by Subrah- manyam (in 1995) in fuzzy metric spaces to prove an analogues version of Jungck result. In this paper, we prove common xed point theorems for a pair of self-maps by introducing a new contraction which neither requires completeness of spaces nor continuity and compatible property of maps. An example is given in support of our main result.
Abstract
After the inspirational innovation of fuzzy set by Zadeh in 1965, Kramosil and Michalek in 1975 pioneered the concept of fuzziness in metric spaces and very rst they formulated the notion of fuzzy met- ric spaces. Jungck introduced the idea of commutativity (in 1976) and compatibility (1986) in metric spaces and same are utilized by Subrah- manyam (in 1995) in fuzzy metric spaces to prove an analogues version of Jungck result. In this paper, we prove common xed point theorems for a pair of self-maps by introducing a new contraction which neither requires completeness of spaces nor continuity and compatible property of maps. An example is given in support of our main result.
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