On interpolative type multiple fixed points, their geometry and applications on s-metric spaces

Abstract

The survival of a unique fixed point plays a central role in metric fixed point theory and has numerous applications in day-to-day life. However, if a self map has multiple fixed points, then looking at the geometry of the collection of fixed points is extremely appealing and natural. As a result, it is interesting to study the fixed figure problems utilizing interpolative techniques via S-metric spaces. In the present work, we examine novel hypotheses to explore the geometry of the collection of fixed points by establishing the existence of multiple fixed points via interpolative technique in S-metric spaces. Further, we exclude the possibility of an identity map in fixed circle (disc) conclusions. We verify the established conclusions by non-trivial illustrative examples. We conclude the work by discussing the parametric rectified linear unit activation function which is beneficial in the study of neural networks and solving integral equations which is beneficial in numerous mathematical models.