About this article
Published Online: Dec 30, 2021
Page range: 427 - 441
DOI: https://doi.org/10.2478/ausm-2021-0026
Keywords
© 2021 Nihal Özgür et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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.