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 develop a new technique by means of 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.

Keywords

• discontinuity
• fixed point
• s-metric
• fixed-circle problem
• primary 54h25
• secondary 47h09, 47h10