Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : A fixed point theorem for a special class of probabilistic contraction | Dosenovic et al. Fixed Point Theory and Applications 2011 2011 74 http content 2011 1 74 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access A fixed point theorem for a special class of probabilistic contraction Tatjana Dosenovic Aleksandar Takaci Dusan Rakic and Mirjana Brdar Correspondence dosenovic@ Faculty of Technology University of Novi Sad Bulevar cara Lazara 1 Novi Sad Serbia Springer Abstract In this paper a special class of probabilistic contraction will be considered. Using the theory of countable extension of f-norms we proved a fixed point theorem for such a class of mappings f S S where S F T is a Menger space. Mathematics Subject Classification 2000 54H25 47H10 Keywords fixed point Menger space f-norm probabilistic q-contraction q-contrac-tion A -type strong bn-contraction 1 Introduction The notion of a probabilistic metric spaces is introduced in 1942 by K. Menger. The first idea of K. Menger was to use distribution function instead of nonnegative real numbers as values of the metric. Since then the theory of probabilistic metric spaces has been developed in many directions 1 . The Banach fixed point theorem for contraction mappings has been generalized in different ways see for example 2-7 . For example Mihet 4 has worked on the existence and the uniqueness of fixed points of Sehgal contraction Lj. Ciric at all in 2 worked on a concept of monotone generalized contraction in partially ordered probabilistic metric spaces. Many interesting fixed point results for contraction mappings for singlevalued and multivalued mappings in probabilistic metric spaces can be found in 8 . First we shall give some definitions and notations. Definition 1 9 The ordered pair S F is said to be a probabilistic metric space if S is a nonempty set and F S X S A A is the set of all distribution functions F such that F 0 0 so that the following conditions are satisfied where F p q is written by .
