Turkish Journal of Mathematics
Abstract
We study on the Rhoades' question concerning the discontinuity problem at fixed point for a self-mapping T of a metric space. We obtain a new solution to this question. Our result generalizes some recent theorems existing in the literature and implies the uniqueness of the fixed point. However, there are also cases where the fixed point set of a self-mapping contains more than 1 element. Therefore, by a geometric point of view, we extend the Rhoades' question to the case where the fixed point set is a circle. We also give a solution to this extended version.
DOI
10.3906/mat-1912-80
Keywords
Metric space, fixed point, fixed circle, discontinuity
First Page
1115
Last Page
1126
Recommended Citation
ÇELİK, UFUK and ÖZGÜR, NİHAL
(2020)
"A new solution to the discontinuity problem on metric spaces,"
Turkish Journal of Mathematics: Vol. 44:
No.
4, Article 3.
https://doi.org/10.3906/mat-1912-80
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss4/3
