Convergence Theorems for Generalized Contractions and Applications

Abstract

The principal results in this article deal with the existence of fixed points of a new class of generalized $F$-contraction. Innovative approach of visualizing non-trivial examples gives a new direction especially to nonlinear problems pertinent to geometrical interpretation. Presented results substantially theorize and improve $F$-contraction version of some prime results in the existing literature. In section-4, application to graph theory is entrusted and proved results are endorsed by an example through graph. The presented new techniques give the possibility to justify the existence problems of the solutions for some class of integral equations. For the future aspects of our study, an open problem is suggested regarding discretized population balance model, whose solution may be derived from the established techniques.