@article{article_776463, title={New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem}, journal={Conference Proceedings of Science and Technology}, volume={3}, pages={160–165}, year={2020}, author={Taş, Nihal}, keywords={Fixec circle, Fixed disc, Fixed point, Metric space}, abstract={<div style="text-align:justify;"> <span style="font-size:14px;">Recently, the Rhoades’ open problem which is related to the discontinuity at fixed point of a self-mapping and the fixed-circle problem which is related to the geometric meaning of the set of fixed points of a self-mapping have been studied using various approaches. Therefore, in this paper, we give some solutions to the Rhoades’ open problem and the fixed-circle problem on metric spaces. To do this, we inspire from the
Meir-Keeler type, Ciric type and Caristi type fixed-point theorems. Also, we use the simulation functions and Wardowski’s technique to obtain new fixed-circle results. </span> </div>}, number={1}, publisher={Murat TOSUN}