FIXED POINT FOR FAMILY OF MAPPINGS WITH AN APPLICATION IN DYNAMIC PROGRAMMING

Abstract

In this paper, we investigate the existence of a unique common fixed point of families of weakly compatible mappings along with property(E.A), common limit range property(CLR) and joint common limit range (JCLR) property satisfying a generalized (ψ, φ)-weak contraction condition involving cubic terms of distance function which generalize the result of Ciri´c [7, 8], ´ Ciri´c ´ et al. [9], Chugh and Kumar [10], Jain and Kumar [12] , Jain et al.[14, 16], Jungck [17], Kang et al. [20], Murthy and Prasad [25], Razani and Yazadi [26], Singh and Jain [29] and Zhang and Song [31]. As an application, we discuss the existence and uniqueness of a common solution of certain functional equations arising in dynamic programming.