Fixed point theory in α -complete metric spaces with applications

Abstract

The aim of this paper is to introduce new concepts of α - η -complete metric space and α - η -continuous function and establish fixed point results for modified α - η - ψ -rational contraction mappings in α - η -complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for ψ -graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results. © 2014 N. Hussain et al.