ON THE FIXED-CIRCLE PROBLEM

In this paper, we focus on the geometric properties of fixed-points of a self-mapping and obtain new solutions to a recent problem called "fixed-circle problem" in the setting of an S-metric space. For this purpose, we develop various techniques by defining new contractive conditions and using some auxiliary functions. Furthermore, we present new examples to support our theoretical results

Solving a Boundary Value Problem via Fixed-Point Theorem on ®-Metric Space

In this paper, we prove the fixed-point theorem for rational contractive mapping on ®-metric space. Additionally, an Euclidean metric space with a binary relation example and an application to the first-order boundary value problem are given. Moreover, the obtained results generalize and extend some of the well-known results in the literature.The authors thank the Basque Government for its support of this work through Grant IT1207-19

FIXED POINT SETS OF SELF-MAPPINGS WITH A GEOMETRIC VIEWPOINT

In this paper, we obtain new fixed point results with the help of various techniques constructed by using auxiliary numbers and some family of functions. In the context of the fixed-circle (resp. fixed-disc) problem, we consider the geometry of the fixed point set of a self-mapping on a metric space. Also, we discuss the effectiveness of our theoretical fixed point results by considering possible applications to the study of neural networks

Fixed points and lines in 2-metric spaces

We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.Comment: adds reference