Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations

Abstract

This paper aims to discuss the convergence behavior of fixed points for graphical Bc-Kannan-contractions using numerical iterations within the structure of graphical extended b-metric spaces. We provide innovative fixed point results using Bc-Kannan-contraction and demonstrate that every Kannan contraction is a graphical Bc-Kannan, but the converse is not valid in general. The findings, which explain the convergence of fixed points for graph-Kannan mappings, are the first of their kind in state of the art. We give examples using the framework of graphical analysis to show that our important findings are more general than the research that backs them up. Lastly, utilizing our results, we show that a solution to a fourth-order two-point boundary value problem expressing elastic beam deformations exists.