Some variants of two basic hybrid fixed point theorems of Krasnoselskii and Dhage with applications

Abstract

In this paper we prove some basic hybrid fixed point theorems involving the sum of two operators in a Banach space as well as the product of two operators in a Banach algebra which generalize the hybrid fixed point theorems on the lines of Krasnoselskii (1964) and Dhage (1988). Applications of the newly developed abstract hybrid fixed point theorems are given to nonlinear hybrid linearly perturbed and quadratic integral equations for proving the existence of solution under certain mixed Lipschitz and compactness type conditions.