arXiv subjects

Nihal Taş

Publications and source records attributed to Nihal Taş.

15 recordsLinked to original sources

arXiv2021

New Fixed Figure Results with the Notion of $k$-Ellipse

In this paper, as a geometric approach to the fixed-point theory, we prove new fixed-figure results using the notion of $k$-ellipse on a metric space. For this purpose, we are inspired by the Caristi type contraction, Kannan type contraction, Chatterjea type contraction and Ćirić type contraction. After that, we give some existence and uniqueness theorems of a fixed $k$-ellipse. We also support our obtained results with illustrative examples. Finally, we present a new application to the $S$-Shaped Rectified Linear Activation Unit ($SReLU$) to show the importance of our theoretical results.

math.MG↗

arXiv2021

A Geometric Interpretation to Fixed-Point Theory on $S_{b}$-Metric Spaces

In this paper we present some fixed-figure theorems as a geometric approach to the fixed-point theory when the number of fixed points of a self-mapping is more than one. To do this, we modify the Jleli-Samet type contraction and define new contractions on $S_{b}$-metric spaces. Also, we give some necessary examples to show the validity of our theoretical results. Keywords: Fixed figure, fixed disc, fixed ellipse, fixed hyperbola, fixed Cassini curve, fixed Apollonius circle.

math.MG↗

arXiv2021

$φ$-fixed points of self-mappings on metric spaces with a geometric viewpoint

A recent open problem was stated on the geometric properties of $φ$-fixed points of self-mappings of a metric space in the non-unique fixed point cases. In this paper, we deal with the solutions of this open problem and present some solutions via the help of appropriate auxiliary numbers and geometric conditions. We see that a zero of a given function $φ$ can produce a fixed circle (resp. fixed disc) contained in the fixed point set of a self-mapping $T$ on a metric space. Moreover, this circle (resp. fixed disc) is also contained in the set of zeros of the function $φ$.

math.GN↗

arXiv2021

Geometric Properties of Fixed Points and Simulation Functions

Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a geometric figure. In this paper, we consider the set of simulation functions for geometric applications in the fixed point theory both on metric and some generalized metric spaces ($S$-metric spaces and $b$-metric spaces). The main motivation of this paper is to investigate the geometric properties of non unique fixed points of self-mappings via simulation functions.

math.MG↗

arXiv2019

New Multivalued Contractions and the Fixed-Circle Problem

In this paper, we focus on the fixed-circle problem on metric spaces by means of the multivalued mappings. We introduce new multivalued contractions using Wardowski's techniques and obtain new fixed-circle results related to multivalued contractions with some applications to integral type contractions. We verify the validity of our obtained results with illustrative examples.

math.MG↗

arXiv2019

A New Solution to the Rhoades' Open Problem with an Application

We give a new solution to the Rhoades' open problem on the discontinuity at fixed point via the notion of an $S$-metric. To do this, we inspire with the notion of a Zamfirescu mapping. Also, we consider a recent problem called the "fixed-circle problem" and propose a new solution to this problem as an application of our technique.

math.FA↗

arXiv2019

Pata Zamfirescu Type Fixed-Disc Results with a Proximal Application

This paper is concerning to the geometric study of fixed points of a self-mapping on a metric space. We establish new generalized contractive conditions which ensure that a self-mapping has a fixed disc or a fixed circle. We introduce the notion of a best proximity circle and explore some proximal contractions for a non-self-mapping as an application. Necessary illustrative examples are presented to highlight the importance of the obtained results.

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

On the topological equivalence of S-metric and cone S-metric spaces

The aim of this paper is to establish the equivalence between the concepts of an $S$-metric space and a cone $S$-metric space using\ some topological approaches. We introduce a new notion of $TVS$-cone $S$-metric space using some facts about topological vector spaces. We see that the known results on cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained from the studies on $S$-metric spaces.

math.GN↗

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

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

Pell Coding and Pell Decoding Methods with Some Applications

We obtain a new coding and decoding method using the generalized Pell $(p,i)$ -numbers. The relations among the code matrix elements, error detection and correction have been established for this coding theory. We give two new blocking algorithms using Pell numbers and generalized Pell $(p,i)$-numbers.

math.NT↗

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↗