A fixed point theorem for weakly compatible mappings satisfying a general contractive condition of operator type

Abstract

In this paper, we prove a fixed point theorem for weakly compatible mappings satisfying a general contractive condition of operator type. In short, we are going to study mappings A, B,S,T : X -> X for which there exists a right continuous function psi : R+-> R+, psi(0) = 0 and psi(s) < s for s > 0 such that for each x, y is an element of X one has O(f; d(S-x,T-y))<= psi(O(f; M(x,y))), where O(f;.) and f are defined in the first section. Also in the first section, we give some examples for O(f;). The second section contains the main result. In the last section, we give some corollaries and remarks.