Nihal Yilmaz Özgür

Some Generalizations of Fixed-Point Theorems on S -MetricSpaces

In this paper we prove new fixed-point theorems on complete S-metric spaces. Our results generalize and extend some fixed-point theorems in the literature. We give some examples to show the validity of our fixed-point results.

Some Fixed-Circle Theorems on Metric Spaces

The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We verify our results by illustrative examples.

On Parametric -Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings

We introduce the notion of a parametric -metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametric -metric space. It is important to obtain new fixed-point theorems on a parametric -metric space because there exist some parametric -metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametric -metric space.

Relationships between fixed points and eigenvectors in the group GL(2,R)

AbstractPSL(2,R) is the most frequently studied subgroup of the Möbius transformations. By adding anti-automorphisms G′={a′z+b′c′z+d′:a′,b′,c′,d′∈R,a′d′−b′c′=−1} to the group PSL(2,R), the group G=PSL(2,R)∪G′ is obtained. The elements of this group correspond to matrices of GL(2,R). In this study, we consider the relationships between fixed points of the elements of the group G and eigenvectors of matrices corresponding to the elements of this group.MSC:20H10, 15A18.

Generalizations of Metric Spaces: From the Fixed-Point Theory to the Fixed-Circle Theory

This paper is a research survey about the fixed-point (resp. fixed-circle) theory on metric and some generalized metric spaces. We obtain new generalizations of the well-known Rhoades’ contractive conditions, Ciri c’s fixed-point result and Nemytskii-Edelstein fixed-point theorem using the theory of an Sb-metric space. We present some fixed-circle theorems on an Sb -metric space as a generalization of the known fixed-circle (fixed-point) results on a metric and an S-metric space.

Wardowski Type Contractions and the Fixed-Circle Problem on -Metric Spaces

In this paper, we present new fixed-circle theorems for self-mappings on an -metric space using some Wardowski type contractions, -contractive, and weakly -contractive self-mappings. The common property in all of the obtained theorems for Wardowski type contractions is that the self-mapping fixes both the circle and the disc with the center and the radius .

Some fixed-circle theorems and discontinuity at fixed circle

In this study, we give some existence and uniqueness theorems for fixed circles of self-mappings on a metric space with some illustrative examples. Recently, real-valued neural networks with discontinuous activation functions have been a great importance in practice. Hence we give some new results for discontinuity at fixed circle on a metric space.

On the Circle Preserving Property of Möbius Transformations

This paper is mainly concerned with the study of circle-preserving property of Mobius transformations acting on \(\widehat{\mathbf{R}}^{n}=\mathbf{R} ^{n}\cup \left\{\infty \right\}\). The circle-preserving property is the most known invariant characteristic property of Mobius transformations. Obviously, a Mobius transformation acting on \(\widehat{\mathbf{R}}^{n}\) is circle-preserving. Recently, for the converse statement, some interesting and nice results have been obtained. Here, we investigate these studies. We consider the relationships between Mobius transformations and sphere-preserving maps in \(\widehat{\mathbf{R}} ^{n}\) since the studies about the circle-preserving property of maps in \(\widehat{\mathbf{R}}^{n}\) are related to the study of sphere-preserving maps. For the case n = 2, we also consider the problem whether or not the circle-preserving property is an invariant characteristic property of Mobius transformations for the circles corresponding to any norm function \(\left\Vert.\right\Vert\) on \(\mathbf{C}\).