New contributions to nonunique fixed-point results via power type contractions

Abstract

The geometry of fixed point set F ix(T) has been studied with different approaches under the fixed-circle problem. To obtain solutions related to this open problem, some known contractive conditions have been modified on metric or generalized metric spaces. In this paper, our aim is to investigate new fixed-circle results using the power type contractions on a metric space and generalize some theorems in the literature. All the obtained theoretical results are supported by various examples. Finally, we present an application to Exponential Linear Unit (ELU) Derivative which is used in neural networks as an activation function. It is hoped this study will give information about new solutions about fixed-circle problem and will shed light on new research topics.