On fixed point and its application to the spread of infectious diseases model in Mvb- metric space

Abstract

This work aims to prove new results in an M v b - metric space for a noncontinuous single-valued self-map. As a result, we extend, generalize, and unify various fixed-point conclusions for a single-valued map and come up with examples to exhibit the theoretical conclusions. Further, we solve a mathematical model of the spread of specific infectious diseases as an application of one of the conclusions. In the sequel, we explain the significance of M v b - metric space because the underlying map is not necessarily continuous even at a fixed point in M v b - metric space thereby adding a new answer to the question concerning to continuity at a fixed point posed by Rhoades’. Consequently, we may conclude that the results via M v b - metric are very inspiring, and underlying contraction via M v b - metric does not compel the single-valued self-map to be continuous even at the fixed point. Our research is greatly inspired by the exciting possibilities of using noncontinuous maps to solve real-world nonlinear problems.