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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 647-655, October 2007




FIXED POINTS IN FUZZY METRIC SPACE FOR

NONCOMPATIBLE MAPS


BY


VYOMESH PANT AND R. P. PANT




Abstract. The present paper is aimed at obtaining common fixed point theorems in fuzzy metric space for a pair of selfmaps by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved. We also find an affirmative answer in fuzzy metric space to the problem of Rhoades (see page 245 in [16]).

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Received November 18, 2005.

AMS Subject Classification. 47H10, 54H25.

Key words. fuzzy metric space, noncompatible mappings, R-weak commutativity, common fixed point.