On Uniform Exhuastiveness and Korovkin-type Theorem

Erdem, Alper | Tunç, Tuncay | Arpacıoğlu, Ali

This study considers a uniform version of exhaustiveness for function sequences and examined its connections with alpha convergence, uniform alpha convergence, and classical uniform convergence. A Korovkin-type approximation theorem is also established, showing that the classical conditions can be loosened under this new concept.

ANALYSIS OF CONICS UNDER KANTOROVICH OPERATORS OF TWO VARIABLES

Elkahwa, Esraa Dakak | Tunç, Tuncay

This study examines some shape-preserving properties of two-variable Kantorovich polynomials. We examine which types of conic equations transform into conic equations under two types of two-variable Kantorovich polynomials, single-index and double-index, and if so, which conic equations they transform into. While it is observed that conic equations transform into the same type of conic equations under the single-index two-variable Kantorovich polynomial, they are shown to transform into different types under the double-index two-variable Kantorovich polynomial, for example, a circle can transform into an ellipse or parabola under certain conditions. Furthermore, all the  findings are supported by numerous graphical examples.

On Cauchy alpha and uniform alpha convergence

Erdem, Alper | Tunç, Tuncay

In this paper we introduced the notions of Cauchy alpha convergence and uniform alpha convergence for sequences of functions between metric spaces. Using these new concepts, we investigated properties between uniform convergence and alpha convergence and provided figures illustrating the relationships among these different types of convergence based on the structure of the functions and their domains. Finally, we established some Korovkin-type approximation theorems involving these new concepts.

Korovkin-type theorems via some modes of convergence

Erdem, Alper | Tunç, Tuncay

In this study, we investigate the Korovkin-type theorems depending upon some type of convergence such as alpha convergence, semi-alpha convergence and the notion of exhaustiveness. Since it is known that the convergence types mentioned above are between point-wise convergence and uniform convergence, it will be observed that the conditions can be alleviated in the Korovkin theorem.

Whitney eşitsizliği ve uygulamaları

Tunç, Tuncay

On Semi-Exhaustiveness, Semi-Uniform Convergence and Korovkin-Type Theorems

Erdem, Alper | Tunç, Tuncay

In this study, we scrutinize the Korovkin-type theorems based on various forms of convergence, such as almost uniform convergence, semi-uniform convergence, and the concept of semi-exhaustiveness. Since it is known that the convergence types mentioned above are between point-wise and uniform convergence, it will be noticed that the circumstances can be mitigated in the Korovkin theorem.

On Filter Convergence and Its Applications to Convergence Theorems

Erdem, Alper | Tunç, Tuncay

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On Some Generalizations of Cholodowsky Type Szasz-Mirakjan-Bernstein Operators

Tunç, Tuncay | Fedakar, Burcu

In this paper, we introduced two different Stancu-type generalizations of Chlodovsky-type Szasz-Mirakyan-Bernstein operators. We gave a general moment formula for these operators. We investigated the approximation properties and obtained the rate of convergence by means of modulus of continuity. Also, Voronovskaja-type theorems were obtained.

On some semi-convergences with applications on Korovkin-type theorems

Erdem, Alper | Tunç, Tuncay

On some semi-convergences with applications on Korovkin-type theorems

A note on convergence theorems for integrals

Tunç, Tuncay | Erdem, Alper

In this study we investigate the convergence theorems such as bounded convergence theorem, Fatou’s lemma, monotone convergence theorem and dominated convergence theorem for measurable functions depending upon the concept of statistical convergence.

SOME CONVERGENCE TYPES OF FUNCTION SEQUENCES AND THEIR RELATIONS

Erdem, Alper | Tunç, Tuncay

In this paper, we investigate various types of convergence for sequences of functions and examine the relationships among these types. Our ndings contribute to a deeper understanding of the structural properties of function sequences and their convergence behaviors.

On statistically convergence theorems for Lebesgue integrable functions

Erdem, Alper | Tunç, Tuncay

On statistically convergence theorems for Lebesgue integrable functions

Yaklaşım teorisinde Whitney sabitleri üzerine

Tunç, Tuncay

ÖZ: Bu çalışmada, Whitney sabitleri, Whitney interpolasyon sabitleri ve Kryakin sabitleri hakkında detaylı bilgiler verildi. Whitney interpolasyon sabitlerinin 3 ile, Whitney ve Kryakin sabitlerinin ise 2.14 ile üstten sınırlı olduğu gösterildi. ABSTRACT: In this work, it was given detailed information about Whitney constants, Whitney interpolation constants and Kryakin constants. It was shown that Whitney interpolation constants are bounded by 3, Whitney and Kryakin constants are bounded by 2.14. Key words: Whitney constants, interpolation, polynomial approximation.

A Note on Convergence Theorems For Integrals

Tunç, Tuncay

In this study we investigate the convergence theorems such as bounded convergence theorem, Fatou’s lemma, monotone convergence theorem and dominated convergence theorem for measurable functions depending upon the concept of statistical convergence.

On Semi Uniform Alpha Convergence and a Korovkin-Type Theorem

Erdem, Alper | Arpacıoğlu, Ali | Tunç, Tuncay

In this paper, we introduce the notion of semi uniform alpha convergence for sequences of functions between metric spaces. We also provide some results concerning the relationship between uniform exhaustiveness, semi uniform exhaustiveness and semi uniform alpha convergence. Finally, we give a Korovkin-type theorem related to uniform exhaustiveness.