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

Abstract

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.