Abstract
The aim of this paper is to introduce new concepts of alpha-eta-complete metric space and alpha-eta-continuous function and establish fixed point results for modified alpha-eta-psi-rational contraction mappings in alpha-eta-complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for psi-graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.