<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

A new solution to the Rhoades’ open problem with an application

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"A new solution to the Rhoades\u2019 open problem with an application"}

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...

A new solution to the Rhoades’ open problem with an application

Published Online: Dec 30, 2021

Page range: 427 - 441

DOI: https://doi.org/10.2478/ausm-2021-0026

Keywords
discontinuity, fixed point, S-metric, fixed-circle problem

© 2021 Nihal Özgür et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A new solution to the Rhoades’ open problem with an application

Published Online: Dec 30, 2021

Page range: 427 - 441

DOI: https://doi.org/10.2478/ausm-2021-0026

Keywordsdiscontinuity, fixed point, S-metric, fixed-circle problem

© 2021 Nihal Özgür et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
discontinuity, fixed point, S-metric, fixed-circle problem