Revisiting some popular contractive conditions for the fixed-circle problem

Abstract

The main aim of this paper is to present some fixed-disc theorems as new solutions to the fixed-circle problem. For this purpose, we define the notions of Moradi type a(0)-contraction, Geraghty type a(0)- contraction, Jleli-Samet type a(0)-contraction, Skof type a(0)-contraction and Li-Jiang type a(0)-contraction modifying the some known contractive conditions which are used to obtain fixed-point theorems. Also, we give an equivalent theorem of some contractions. Finally, we present an application to the rectified linear unit (ReLU) activation function.