Fixed Point Theory, 14(2013), No. 2, 497-506 http://www.math.ubbcluj.ro/ ∼ nodeacj/sfptcj.html SUZUKI TYPE COMMON FIXED POINT THEOREMS AND APPLICATIONS SHYAM LAL SINGH * , RENU CHUGH ** AND RAJ KAMAL *** * L. M. S. Govt. Autonomous Postgraduate College Rishikesh 249201, India E-mail: vedicmri@gmail.com **,*** Department of Mathematics, Maharshi Dayanand University Rohtak 124001, India E-mail: ** chughrenu@yahoo.com, *** rajkamalpillania@yahoo.com Abstract. Common fixed point theorems for Suzuki type conditions for a pair of maps on a metric space are obtained. Existence of a common solution for a class of functional equations arising in dynamic programming is also discussed. Key Words and Phrases: Fixed point; Banach contraction theorem, functional equations, dy- namic programming. 2010 Mathematics Subject Classification: 47H10, 54H25. 1. Introduction Generalizing the classical Banach contraction theorem (Bct) and some other results by Chatterjea [5], Hardy and Rogers [8], Kannan [10], Reich [15], Rus [17] and others, Wong [24] obtained the following common fixed point theorem for a pair of maps on a complete metric space. Theorem 1.1 Let S and T be maps from a complete metric space (X, d) to itself. Suppose that their exist nonnegative real numbers a 1 ,a 2 ,a 3 ,a 4 ,a 5 which satisfy (i) a 1 + a 2 + a 3 + a 4 + a 5 < 1; (ii) a 2 = a 3 or a 4 = a 5 . Assume for each x, y ∈ X, (iii) d(Sx,Ty) ≤ a 1 d(x, y)+ a 2 d(x,Sx)+ a 3 d(y,Ty)+ a 4 d(x, T y)+ a 5 d(y,Sx). Then S and T have a unique common fixed point. Recently Suzuki [23] obtained a forceful generalization of the Bct. It has several important outcomes and applications (see, for instance, [6, 7, 11, 12, 14, 20, 22]). The following generalization of the Bct is essentially due to Mot ¸ and Petru¸sel [12]. * Corresponding author’s address: 21, Govind Nagar, Rishikesh 249201, India. Tel.:+91-135-2431624 E-mail: vedicmri@gmail.com. 497