New fixed point theorems for θ - ϕ -contraction on b -metric spaces

Abstract

In this paper, we define \(\theta\)-\(\phi\)-contraction on a \(b\)-metric space into itself by extending \(\theta\)-\(\phi \)-contraction introduced by Zheng {et al.} [D. W. Zheng, Z. Y. Cai, P. Wang, J. Nonlinear Sci. Appl., \(\bf 10\) (2017), 2662--2670] in metric space and also, we prove \(\theta \)-type theorem in the setting of \(b\)-metric spaces as well as \(\theta\)-\(\phi \)-type theorem in the framework of \(b\)-rectangular metric spaces. Moreover, we give some applications to nonlinear integral equations. We also give illustrative examples to exhibit the utility of our results.