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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 875-884, October 2007




WEAKLY COMPATIBLE MAPS IN GENERALIZED

MENGER-PM-SPACES


BY


SANJAY KUMAR




Abstract. The aim of this paper is to generalize the result of Dhage [4] in the setting of probabilistic D-metric spaces , introduced by Chugh, Kumar and Vats (Math Science Research Journal, 7(2003) no 2., 41-48, MR 2003m: 47104). In fact, a generalized probabilistic metric space (briefly GPM-space) is a generalization of a D- metric space in probabilistic setting i.e., the case where instead of the distance between two or more points one knows only the probability of a possible value of this distance and distance is represented by distribution function. At the end, we provide an example in support of our theorem.

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Received November 27, 2006; revised April 11, 2007; June 19, 2007; June 22, 2007.

AMS Subject Classification. 47H10, 54H25.

Key words. generalized menger PM-space, weakly compatible maps.