Interpolative Kannan-type contractions in strong b-metric spaces

Abstract

It can be said that fixed-point theory originated from the research of Brouwer in 1912 and Banach in 1922. Among these, Banach's Fixed Point Theorem plays a central role in this theory, providing a sufficient condition for a mapping from a complete metric space into itself to have a unique fixed point. Banach's Fixed Point Theorem is also an important tool for studying the existence of solutions to differential equations, systems of linear equations, integral equations, and various other applications. In this paper, we improve Banach's Fixed Point Theorem from an interpolation perspective in strong -metric spaces. By using the concept of interpolation, we propose a new type of contraction mapping on extended metric spaces. The results obtained in the paper are generalizations of Kannan's results. Additionally, an example is provided to illustrate the theoretical results.