A New Solution to the Rhoades' Open Problem with an Application

Abstract

We give a new solution to the Rhoades' open problem on the discontinuity at fixed point via the notion of an $S$-metric. To do this, we inspire with the notion of a Zamfirescu mapping. Also, we consider a recent problem called the "fixed-circle problem" and propose a new solution to this problem as an application of our technique.