New classes of control functions for nonlinear contractions and applications

Abstract

We initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.