On Unique and Nonunique Fixed Points in Metric Spaces and Application to Chemical Sciences

Abstract

We introduce the notions of a generalized $\Theta$ -contraction, a generalized ${\Theta }_{\mathcal{E}}$ -weak contraction, a ${\Psi }_{\mathcal{E}}$ -weak JS-contraction, an integral-type ${\Theta }_{\mathcal{E}}$ -weak contraction, and an integral-type ${\Psi }_{\mathcal{E}}$ -weak JS-contraction to establish the fixed point, fixed ellipse, and fixed elliptic disc theorems. Further, we verify these by illustrative examples with geometric interpretations to demonstrate the authenticity of the postulates. The motivation of this work is the fact that the set of nonunique fixed points may include a geometric figure like a circle, an ellipse, a disc, or an elliptic disc. Towards the end, we provide an application of $\Theta$ -contraction to chemical sciences.