Fixed point results for alpha-implicit contractions with application to integral equations

Abstract

Recently, Aydi et al. [On fixed point results for alpha-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21(1):40-56, 2016] proved some fixed point results involving alpha-implicit contractive conditions in quasi-b-metric spaces. In this paper we extend and improve these results and derive some new fixed point theorems for implicit contractions in ordered quasi-b-metric spaces. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.