Sevda YILDIZ | Sinop Üniversitesi (original) (raw)

Papers by Sevda YILDIZ

Indian Journal of Pure and Applied Mathematics, 2021

Facta Universitatis, Nov 1, 2020

We will obtain an abstract version of the Korovkin type approximation theorems with respect to th... more We will obtain an abstract version of the Korovkin type approximation theorems with respect to the concept of statistical relative convergence in modular spaces for double sequences of positive linear operators. We will give an application showing that our results are stronger than classical ones. We will also study an extension to non-positive operators.

Communications Faculty of Sciences University of Ankara. Series A1: mathematics and statistics, Jan 10, 2020

The aim of the present paper is to de…ne Ka continuity which is associated to the number sequence... more The aim of the present paper is to de…ne Ka continuity which is associated to the number sequence a = (an) and to give some new results.

Bulletin of the Malaysian Mathematical Sciences Society, Jan 28, 2020

In this work, we obtain a Korovkin-type approximation theorem for double sequences of real-valued... more In this work, we obtain a Korovkin-type approximation theorem for double sequences of real-valued functions by using the power series method in two-dimensional weighted spaces. We also study the rate of convergence by using the weighted modulus of continuity, and in the last section, we present an application that satisfies our new Korovkin-type approximation theorem but does not satisfy classical one.

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, Jan 22, 2022

The Korovkin theory has effective role in approximation theory. This theory is connected with the... more The Korovkin theory has effective role in approximation theory. This theory is connected with the approximation to continuous functions by means of positive linear operators. Many mathematicians have investigated the Korovkin-type theorems by for a sequence of positive linear operators defined on different spaces by using various types of convergence. Firstly, A.D. Gadjiev has proved the weighted Korovkin type theorems, (Math. Zamet., 20 (1976) 781-786 (in Russian)). Later, these theorems are studied by many authors by means of different convergence methods. Recently, The definition of equal convergence for real functions was introduced by Császár and Laczkovich and they improved their investigations on this * convergence. Later Das et. al. introduced the ideas of I and I-equal convergence with the help of ideals by extending the equal convergence (Mat. Vesnik, vol:66, 2 (2014),165-177). In our work, we introduce a new type of statistical convergence on weighted spaces by using the notions of the equal convergence. We study its use in the Korovkin-type approximation theory. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work.

Classical approximation theory has started with the proof of Weierstrass approximation theorem an... more Classical approximation theory has started with the proof of Weierstrass approximation theorem and after that Korovkin [Linear operators and approximation theory, Hindustan Publ. Corp, Delhi, 1960] first established the necessary and sufficient conditions for uniform convergence of a sequence of positive linear operators to a function f. In classical Korovkin theorem, most of the classical operators tend to converge to the value of the function being approximated. Also, the attention of researchers has been attracted to the notion of statistical convergence because of the fact that it is stronger than the classical convergence method. Furthermore, the concept of equi-statistical convergence is more general than the statistical uniform convergence. In this work, we introduce our new convergence method named equi-statistical relative convergence to demonstrate a Korovkin type approximation theorems which were proven by earlier authors. Then, we present an example in support of our definition and result presented in this paper. Finally, we compute the rate of the convergence.

Positivity, Mar 7, 2019

We prove a Korovkin-type approximation theorem using the relative uniform convergence of a sequen... more We prove a Korovkin-type approximation theorem using the relative uniform convergence of a sequence of functions at a point, which is a method stronger than the classical ones. We give some examples on this new convergence method and we study also rates of convergence.

Publications De L'institut Mathematique, 2021

We introduce some notions of variation using the statistical convergence with respect to power se... more We introduce some notions of variation using the statistical convergence with respect to power series method. By the use of the notions of variation, we prove criterions that can be used to verify convergence without using limit value. Also, some results that give relations between P-statistical variations are studied.

Lobachevskii Journal of Mathematics

Rendiconti del Circolo Matematico di Palermo Series 2

Georgian Mathematical Journal, 2020

In this paper, we introduce an interesting kind of convergence for a double sequence called the u... more In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in the last section, we compute the rate of convergence.

4th International Symposium on Innovative Approaches in Engineering and Natural Sciences Proceedings, 2019

Korovkin type approximation theorems have very important role in the approximation theory. Many m... more Korovkin type approximation theorems have very important role in the approximation theory. Many mathematicians investigate and improve these type of approximation theorems for various operators defined on different spaces via several new convergence methods. The convergence of a sequence of positive linear operators defined on weighted space was first studied by Gadjiev [Theorems of Korovkin type, Math. Zametki 20(1976), 781-786]. Then, these results were improved by many authors for different type of convergence methods. Recently, some authors study Korovkin type theorems for two variables functions by means of single and double sequences on weighted spaces. In this paper, we prove a Korovkin type approximation theorem for the notion of statistical equal convergence for double sequences on two dimensional weighted spaces. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work. Also, we compute the rate of stati...

Mathematical Methods in the Applied Sciences, 2018

In this paper, we study the Korovkin type approximation theorem for Ka‐ convergence, which is an ... more In this paper, we study the Korovkin type approximation theorem for Ka‐ convergence, which is an interesting convergence method on weighted spaces. We also study the rate of Ka−convergence by using the weighted modulus of continuity and afterwards, we present a nontrivial application.

Annals of the University of Craiova - Mathematics and Computer Science Series, Jun 30, 2021

In this paper, we give statistical Voronoi mean which is a new statistical summability method, is... more In this paper, we give statistical Voronoi mean which is a new statistical summability method, is not need to be regular and positive. We prove a Korovkin type approximation theorem via this method that covers many important summability methods scattered in the literature. Also, we demonstrate that our theorem is stronger than proved by earlier authors with an interesting application. Finally, we establish the rate of convergence.

Universal Journal of Mathematics and Applications

In the current research, we investigate and establish Korovkin-type approximation theorems for li... more In the current research, we investigate and establish Korovkin-type approximation theorems for linear operators defined on the space of all % 2\pi -periodic and real valued continuous functions on % %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2} by means of mathcalA\mathcal{A}mathcalA-summation process via statistical convergence with respect to power series method. We demonstrate with an example how our theory is more strong than previously studied. Additionally, we research the rate of convergence of positive linear operators defined on this space.

Sinop Üniversitesi Fen Bilimleri Dergisi

In this paper, we first present the notions of statistical relative modular and F-norm convergenc... more In this paper, we first present the notions of statistical relative modular and F-norm convergence concerning the power series method. Then, we also present theorems of Korovkin-type via statistical relative A-summation process via power series method on modular spaces, including as particular cases weighted spaces, certain interpolation spaces, Orlicz and Musielak-Orlicz spaces, Lp spaces and many others. Later, we consider some application to Kantorovich-type operators in Orlicz spaces. Moreover, we present some estimates of rates of convergence via modulus of continuity. We end the paper with giving some concluding remarks.

TURKISH JOURNAL OF MATHEMATICS, 2021

In the present paper, using the triangular A− statistical convergence for double sequences, which... more In the present paper, using the triangular A− statistical convergence for double sequences, which is an interesting convergence method, we prove a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on [0, ∞) × [0, ∞) with the property that have a finite limit at the infinity. Moreover, we present the rate of convergence via modulus of continuity. Finally, we give some further developments.

Indian Journal of Pure and Applied Mathematics, 2021

Facta Universitatis, Nov 1, 2020

We will obtain an abstract version of the Korovkin type approximation theorems with respect to th... more We will obtain an abstract version of the Korovkin type approximation theorems with respect to the concept of statistical relative convergence in modular spaces for double sequences of positive linear operators. We will give an application showing that our results are stronger than classical ones. We will also study an extension to non-positive operators.

Communications Faculty of Sciences University of Ankara. Series A1: mathematics and statistics, Jan 10, 2020

The aim of the present paper is to de…ne Ka continuity which is associated to the number sequence... more The aim of the present paper is to de…ne Ka continuity which is associated to the number sequence a = (an) and to give some new results.

Bulletin of the Malaysian Mathematical Sciences Society, Jan 28, 2020

In this work, we obtain a Korovkin-type approximation theorem for double sequences of real-valued... more In this work, we obtain a Korovkin-type approximation theorem for double sequences of real-valued functions by using the power series method in two-dimensional weighted spaces. We also study the rate of convergence by using the weighted modulus of continuity, and in the last section, we present an application that satisfies our new Korovkin-type approximation theorem but does not satisfy classical one.

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, Jan 22, 2022

The Korovkin theory has effective role in approximation theory. This theory is connected with the... more The Korovkin theory has effective role in approximation theory. This theory is connected with the approximation to continuous functions by means of positive linear operators. Many mathematicians have investigated the Korovkin-type theorems by for a sequence of positive linear operators defined on different spaces by using various types of convergence. Firstly, A.D. Gadjiev has proved the weighted Korovkin type theorems, (Math. Zamet., 20 (1976) 781-786 (in Russian)). Later, these theorems are studied by many authors by means of different convergence methods. Recently, The definition of equal convergence for real functions was introduced by Császár and Laczkovich and they improved their investigations on this * convergence. Later Das et. al. introduced the ideas of I and I-equal convergence with the help of ideals by extending the equal convergence (Mat. Vesnik, vol:66, 2 (2014),165-177). In our work, we introduce a new type of statistical convergence on weighted spaces by using the notions of the equal convergence. We study its use in the Korovkin-type approximation theory. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work.

Classical approximation theory has started with the proof of Weierstrass approximation theorem an... more Classical approximation theory has started with the proof of Weierstrass approximation theorem and after that Korovkin [Linear operators and approximation theory, Hindustan Publ. Corp, Delhi, 1960] first established the necessary and sufficient conditions for uniform convergence of a sequence of positive linear operators to a function f. In classical Korovkin theorem, most of the classical operators tend to converge to the value of the function being approximated. Also, the attention of researchers has been attracted to the notion of statistical convergence because of the fact that it is stronger than the classical convergence method. Furthermore, the concept of equi-statistical convergence is more general than the statistical uniform convergence. In this work, we introduce our new convergence method named equi-statistical relative convergence to demonstrate a Korovkin type approximation theorems which were proven by earlier authors. Then, we present an example in support of our definition and result presented in this paper. Finally, we compute the rate of the convergence.

Positivity, Mar 7, 2019

We prove a Korovkin-type approximation theorem using the relative uniform convergence of a sequen... more We prove a Korovkin-type approximation theorem using the relative uniform convergence of a sequence of functions at a point, which is a method stronger than the classical ones. We give some examples on this new convergence method and we study also rates of convergence.

Publications De L'institut Mathematique, 2021

We introduce some notions of variation using the statistical convergence with respect to power se... more We introduce some notions of variation using the statistical convergence with respect to power series method. By the use of the notions of variation, we prove criterions that can be used to verify convergence without using limit value. Also, some results that give relations between P-statistical variations are studied.

Lobachevskii Journal of Mathematics

Rendiconti del Circolo Matematico di Palermo Series 2

Georgian Mathematical Journal, 2020

In this paper, we introduce an interesting kind of convergence for a double sequence called the u... more In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in the last section, we compute the rate of convergence.

4th International Symposium on Innovative Approaches in Engineering and Natural Sciences Proceedings, 2019

Korovkin type approximation theorems have very important role in the approximation theory. Many m... more Korovkin type approximation theorems have very important role in the approximation theory. Many mathematicians investigate and improve these type of approximation theorems for various operators defined on different spaces via several new convergence methods. The convergence of a sequence of positive linear operators defined on weighted space was first studied by Gadjiev [Theorems of Korovkin type, Math. Zametki 20(1976), 781-786]. Then, these results were improved by many authors for different type of convergence methods. Recently, some authors study Korovkin type theorems for two variables functions by means of single and double sequences on weighted spaces. In this paper, we prove a Korovkin type approximation theorem for the notion of statistical equal convergence for double sequences on two dimensional weighted spaces. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work. Also, we compute the rate of stati...

Mathematical Methods in the Applied Sciences, 2018

In this paper, we study the Korovkin type approximation theorem for Ka‐ convergence, which is an ... more In this paper, we study the Korovkin type approximation theorem for Ka‐ convergence, which is an interesting convergence method on weighted spaces. We also study the rate of Ka−convergence by using the weighted modulus of continuity and afterwards, we present a nontrivial application.

Annals of the University of Craiova - Mathematics and Computer Science Series, Jun 30, 2021

In this paper, we give statistical Voronoi mean which is a new statistical summability method, is... more In this paper, we give statistical Voronoi mean which is a new statistical summability method, is not need to be regular and positive. We prove a Korovkin type approximation theorem via this method that covers many important summability methods scattered in the literature. Also, we demonstrate that our theorem is stronger than proved by earlier authors with an interesting application. Finally, we establish the rate of convergence.

Universal Journal of Mathematics and Applications

In the current research, we investigate and establish Korovkin-type approximation theorems for li... more In the current research, we investigate and establish Korovkin-type approximation theorems for linear operators defined on the space of all % 2\pi -periodic and real valued continuous functions on % %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2} by means of mathcalA\mathcal{A}mathcalA-summation process via statistical convergence with respect to power series method. We demonstrate with an example how our theory is more strong than previously studied. Additionally, we research the rate of convergence of positive linear operators defined on this space.

Sinop Üniversitesi Fen Bilimleri Dergisi

In this paper, we first present the notions of statistical relative modular and F-norm convergenc... more In this paper, we first present the notions of statistical relative modular and F-norm convergence concerning the power series method. Then, we also present theorems of Korovkin-type via statistical relative A-summation process via power series method on modular spaces, including as particular cases weighted spaces, certain interpolation spaces, Orlicz and Musielak-Orlicz spaces, Lp spaces and many others. Later, we consider some application to Kantorovich-type operators in Orlicz spaces. Moreover, we present some estimates of rates of convergence via modulus of continuity. We end the paper with giving some concluding remarks.

TURKISH JOURNAL OF MATHEMATICS, 2021

In the present paper, using the triangular A− statistical convergence for double sequences, which... more In the present paper, using the triangular A− statistical convergence for double sequences, which is an interesting convergence method, we prove a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on [0, ∞) × [0, ∞) with the property that have a finite limit at the infinity. Moreover, we present the rate of convergence via modulus of continuity. Finally, we give some further developments.