CONTROL FUNCTION FOR COMMON FIXED POINT THEOREM IN COMPLETE 2-MANGER SPACES Surjeet Singh Tomar 1 , M.S. Rathore 2 and Deepak Singh 3 Abstract : In this paper we prove a common fixed point theorem for a class of Kannan type mappings in 2-Menger spaces. Our result generalizes the result of Choudhury et. al.[5] and also generalize some existing fixed point theorems in 2-metric spaces. At the end, an example is also given to validify our theorem. AMS Mathematics subject classification 2000 : 47H 10, 54H 25. Keywords and Phrases : 2-Menger spaces, Weakly compatible maps, Φ-function, Ψ- function, t-norm Δ 1 Introduction Banach contraction mapping principle was proved by S. Banach for metric spaces in 1922. In 1972 this concept was generalized by Sehgal and Bharucha-Reid [32] to probabilistic metric spaces. Probabilistic metric spaces are probabilistic generalization of metric spaces. Subsequently, fixed point theory in probabilistic metric spaces has developed in extensive way. Hadzic and Pap have given a comprehensive survey of this development upto 2001 in [12]. Some of the references in Menger spaces of more recent times may be noted in [22], [26], [27] [28] and [13] Khan et. al.[16] introduced the concept of altering distance function, which is a con- trol function that alters the distance between two points in a metric space. Some of 1 Department of Mathematics, Jai Narayan College of Technology, Bhopal, (M.P.),India, E-mail: stomar.sfsp@gmail.com 2 Department of Mathematics, Chandrashekhar Azad Govt. P.G. College, Sehore, (M.P.), India. 3 Department of Applied Sciences, NITTTR, Under Ministry of HRD, Govt. of India Bhopal,(M.P.),India, 462002. E-mail: dk.singh1002@gmail.com