$\varphi $fixed points of selfmappings on metric spaces with a geometric viewpoint
Abstract
A recent open problem was stated on the geometric properties of $\varphi $fixed points of selfmappings of a metric space in the nonunique fixed point cases. In this paper, we deal with the solutions of this open problem and present some solutions via the help of appropriate auxiliary numbers and geometric conditions. We see that a zero of a given function $\varphi $ can produce a fixed circle (resp. fixed disc) contained in the fixed point set of a selfmapping $T$ on a metric space. Moreover, this circle (resp. fixed disc) is also contained in the set of zeros of the function $\varphi $.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.11199
 Bibcode:
 2021arXiv210711199O
 Keywords:

 Mathematics  General Topology;
 Mathematics  Metric Geometry;
 54H25 (Primary) 47H10;
 55M20 (Secondary)
 EPrint:
 19 pages