arXiv subjects

Nihal Yilmaz Özgür

Publications and source records attributed to Nihal Yilmaz Özgür.

11 recordsLinked to original sources

arXiv2019

Fixed-disc results via simulation functions

In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in our results. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping.

math.MG↗

arXiv2018

Fixed-Circle Problem on S-Metric Spaces with a Geometric Viewpoint

Recently, a new geometric approach which is called the fixed-circle problem has been gained to fixed-point theory. The problem is introduced and studied using different techniques on metric spaces. In this paper, we consider the fixed-circle problem on $S$-metric spaces. We investigate existence and uniqueness conditions for fixed circles of self-mappings on an $S$-metric space. Some examples of self-mappings having fixed circles are also given.

math.MG↗

arXiv2018

A new contribution to discontinuity at fixed point

The aim of this paper is to obtain new solutions to the open question on the existence of a contractive condition which is strong enough to generate a fixed point but which does not force the map to be continuous at the fixed point. To do this, we use the right-hand side of the classical Rhoades' inequality and the number $M(x,y)$ given in the definition of an $(α,β)$-Geraghty type-$I$ rational contractive mapping. Also we give an application of these new results to discontinuous activation functions.

math.MG↗

arXiv2017

Finite Blaschke Products and Decomposition

Let $B(z)$ be a finite Blaschke product of degree $n$. We consider the problem when a finite Blaschke product can be written as a composition of two nontrivial Blaschke products of lower degree related to the condition $% B\circ M=B$ where $M$ is a Möbius transformation from the unit disk onto itself.

math.CV↗

arXiv2017

Right Circulant Matrices with Generalized Fibonacci and\ Lucas Polynomials and Coding Theory

In this paper, we give two new coding algorithms by means of right circulant matrices with elements generalized Fibonacci and Lucas polynomials. For this purpose, we study basic properties of right circulant matrices using generalized Fibonacci polynomials $F_{p,q,n}\left( x\right) $, generalized Lucas polynomials $L_{p,q,n}\left( x\right) $ and geometric sequences.

math.CO↗

arXiv2017

Finite Blaschke Products and the Golden Ratio

It is known that the golden ratio $α=\frac{1+\sqrt{5}}{2}$ has many applications in geometry. In this paper we consider some geometric properties of finite Blaschke products related to the golden ratio.

math.CV↗

arXiv2017

A New Coding/Decoding Algorithm using Fibonacci Numbers

In this paper we present a new method of coding/decoding algorithms using Fibonacci $Q$-matrices. This method is based on the blocked message matrices. The main advantage of our model is the encryption of each message matrix with different keys. Our approach will not only increase the security of information but also has high correct ability.

cs.IT↗

arXiv2017

On the Zeros of $R$-Bonacci Polynomials and Their Derivatives

The purpose of the present paper is to examine the zeros of $R$-Bonacci polynomials and their derivatives. We confirm a conjecture about the zeros of $R$-Bonacci polynomials for some special cases. We also find explicit formulas of the roots of derivatives of $R$-Bonacci polynomials in some special cases.

math.GM↗

arXiv2017

A New Cryptography Model via Fibonacci and Lucas Numbers

Coding/decoding algorithms are of great importance to help in improving information security since information security is a more significiant problem in recent years. In this paper we introduce two new coding/decoding algorithms using Fibonacci $Q$-matrices and $R$-matrices. Our models are based on the blocked message matrices and the encryption of each message matrix with different keys. These new algorithms will not only increase the security of information but also has high correct ability.

cs.CR↗

arXiv2017

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.

math.MG↗

arXiv2017

New Generalized Fixed Point Results on $S_{b}$-Metric Spaces

Recently $S_{b}$-metric spaces have been introduced as the generalizations of metric and $S$-metric spaces. In this paper we investigate some basic properties of this new space. We generalize the classical Banach's contraction principle using the theory of a complete $S_{b}$-metric space. Also we give an application to linear equation systems using the $S_{b}$-metric which is generated by a metric.

math.GN↗