Submetric metric spaces and the fixed point concept

Abstract

Metric spaces form a subfamily of topological spaces, or some appropriate non-empty spaces. The fixed point can, almost always, be found using the Picard iteration (the most widely used fixed point iteration), as one can start from any initial point 0-x in space. Finding fixed points for mappings depends mainly on the settings of the studied spaces, which are defined using some intuitive axioms. Different classes of generalized spaces and several contractions will yield new dynamic research areas and thus different types of uniform fixed point conjectures at once. Most of the effort expended on fixed point theory has been directed at specifying a variety of applicable and easily verifiable sufficient conditions for fixed point problems. The paper consists of a variety of advanced discussions and contemporary topics on metric fixed point theory and its applications to present the feasibility of the results. The research framework undoubtedly contains pure theoretical mathematics. We explore the ideal combination of relaxed conditions to prove our new theorems and realization of the idea in full detail to prove all the results obtained using different, applicable and high-tech proof modes. The results of this research are theoretical and analytical in nature. This study follows the recent trend and latest development in the analysis of metric fixed point theory, and provides a very sound basic text on this theory. This research brings together selected chapters on modern topics of fixed point