New Approach to Find Fixed Point in Extended b-metric Space

Abstract

A fixed point for a suitable map or operator is identical to the presence of a solution to a theoretical or real-world problem. As a result, fixed points are crucial in many fields of mathematics, science, and engineering. In this paper, we establish new fixed point results on self-mappings in setting of extended b-metric space which can be extended further to give application in real world such as in image processing, computer graphics, Nash equilibrium and many more. Our results extends the corresponding results of Mukheimer et. al. [Aimal Mukheimer, Nabil Mlaiki, Kamal Abodayeh, Wasfi Shantanawi, Non Linear Analysis: Modeling and Control, 24(6), 870-883, 2019.] and Kamran et. al. [Tayyab Kamran, Maria Samreen, Qurrat UL Ain, Mathematics, 5(19), 2017, 7 pages.]. Examples are also mentioned to check the authenticity of our results. A solution to Fredholm integral equation is also demonstrated as an application.