New Answers to the Rhoades’ Open Problem and the Fixed-Circle Problem

Year 2020, Volume: 3 Issue: 1, 160 - 165, 15.12.2020

Nihal Taş

Abstract

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.

Keywords

Fixec circle, Fixed disc, Fixed point, Metric space

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