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

In this paper, we define \(θ\)-\(φ\)-contraction on a \(b\)-metric space into itself by extending \(θ\)-\(φ \)-contraction introduced by Zheng {et al.} [D. W. Zheng, Z. Y. Cai, P. Wang, J. Nonlinear Sci. Appl., \( 10\) (2017), 2662--2670] in metric space and also, we prove \(θ \)-type theorem in the setting of \(b\)-metric spaces as well as \(θ\)-\(φ \)-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.