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Common Fixed Point Theorems in Probabilistic Quasi-Metric Spaces
by
Saleh Shakeri
Islamic Azad University-Ayatollah Amoli Branch, Amol P.O. Box 678,Iran
Menger [2] introduced the notion of a probabilistic metric spaces in 1942 and, since then, the theory of probabilistic metric spaces has developed in many directions, especially, in nonlinear analysis and applications [1, 6]. The idea of Menger was to use distribution functions instead of nonnegative real numbers as values of the metric.
Recently, Pathak, Cho and Kang [4] introduced the notion of R-weak commutativity of types (Af) and (Ag) of mappings in metric spaces and proved some common fixed point theorems.
In this paper, we define R-weak commutativity of mapping of types (Af) and (Ag) in probabilistic quasi-metric spaces and prove the probabilistic version of Pathak, Cho and Kang's theorem. In the sequel, we shall adopt usual terminology, notation and conventions of the theory of probabilistic metric spaces, as in [3, 6].
Date received: April 28, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawh-28.