Affiliation:
1. Balıkesir University , Department of Mathematics , 10145 Balıkesir , Turkey
Abstract
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.
Reference33 articles.
1. [1] R. K. Bisht and R. P. Pant, A remark on discontinuity at fixed point, J. Math. Anal. Appl., 445 (2017), 1239–1242.10.1016/j.jmaa.2016.02.053
2. [2] R. K. Bisht and R. P. Pant, Contractive definitions and discontinuity at fixed point, Appl. Gen. Topol., 18 (1) (2017), 173–182.10.4995/agt.2017.6713
3. [3] R. K. Bisht and N. Hussain, A note on convex contraction mappings and discontinuity at fixed point, J. Math. Anal., 8 (4) (2017), 90–96.
4. [4] R. K. Bisht and V. Rakočević, Generalized Meir-Keeler type contractions and discontinuity at fixed point, Fixed Point Theory, 19 (1) (2018), 57–64.10.24193/fpt-ro.2018.1.06
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