Some fixed point results in b-metric spaces approach to the existence of a solution to nonlinear integral equations

Abstract

© 2018, Springer International Publishing AG, part of Springer Nature. The purpose of this paper is to improve some recent fixed point results from Refs. Parvaneh et al. (Sahand Commun Math Anal 7(1):85–104, 2017), Paunović et al. (J Nonlinear Sci Appl 10(8):4162–4174, 2017) and Faraji and Nourouzi (Sahand Commun Math Anal 7(1):49–62, 2017) in the context of b-metric spaces. The techniques used in our proofs are quite different and most remarkably some of the proofs become simpler and more straightforward. Some examples are used to show that the improvements are indeed genuine. In addition, by using our results, we obtain the existence and uniqueness of a solution to a class of nonlinear integral equations. Furthermore, we provide the precise mathematical expression of the solution.