Exploring the potential of inertial type algorithms in solving coincidence point/value problems: Theoretical analysis and practical applications

In this study, we present novel inertial type algorithms designed to address a research gap and provide a solution to an open problem. We focus on a high-performing “Jungck normal-S inertial type algorithm”, which we thoroughly examine for its convergence, stability and data dependency properties. To substantiate our theoretical findings, we include thoughtfully selected numerical examples covering both differential and integral equations. Furthermore, we show case the versatility of these algorithms by employing them to create aesthetically pleasing polynomiographs, enhancing both the educational and artistic dimensions of our work.