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Araştırmacılar Alper Erdem
Arş.Gör. Alper ErdemFEN FAKÜLTESİ MATEMATİK BÖLÜMÜ ANALİZ VE FONKSİYONLAR TEORİSİ ANABİLİM DALI
169215

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.

169214

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.

Makale2025Filomat 60 | 0 Erişime Açık
166724

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.

Makale2024FILOMAT 27 | 0 Erişime Açık
167041

P-Bernstein Polynomials

Erdem, Alper

In this current study, we introduce a new operator called the P− Bernstein operator derived through the utilization of “P-factorial” (Pell factorial) and “Pellnomial” (Pell binomial). Subsequently, we investigate the fundamental properties of the P−Bernstein basis polynomials. Furthermore, we establish some connections between the P-Bernstein Polynomials and Pell Numbers.

Makale2024Filomat 77 | 0 Erişime Açık
167590

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

Erdem, Alper | Tunç, Tuncay

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

167280

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.

167589

On statistically convergence theorems for Lebesgue integrable functions

Erdem, Alper | Tunç, Tuncay

On statistically convergence theorems for Lebesgue integrable functions

167039

General Terms of All Almost Balancing Numbers of First and Second Type

Erdem, Alper

In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms of all balancing numbers in terms of all almost balancing numbers of first and second type. We also set a correspondence between all almost balancing numbers of first and second type and Pell numbers.

167042

On the F-Bernstein polynomials

Erdem, Alper | Dişkaya, Orhan | Menken, Hamza

In this present work, we construct a new Bernstein operator which is called the F -Bernstein operator obtained by using F - factorial (Fibonacci factorial) and Fibonomial (Fibonacci binomial). Then we examine the F-Bernstein basis polynomials and some properties. Moreover, we acquire some connection between the F -Bernstein polynomials and the Fibonacci numbers.

167587

Diferansiyel Denklemler Video Ders Notları

Erdem, Alper

Bu kitap, YouTube’da "Sürekli Matematik" kanalında yayınlanan ve 2,5 milyon izlenmeye ulaşmış diferansiyel denklemler video serisinin detaylı ders notlarını içermektedir. Diferansiyel denklemler konusunu anlamak ve pratik yapmak isteyen öğrenciler için etkileşimli bir eserdir. Adım adım açıklamalar, çözüm teknikleri ve örneklerle dolu bu notlar, okurların konuya hakimiyetini artırmayı hedeflemektedir. Kitap video ders notu biçiminde hazırlanmıştır. Videolarda çözümü yapılan önemli kısımların yerine gri dikdörtgenler çizilerek bu kısımlar tamamlaması için okuyucuya bırakılmıştır.

166740

t-Cobalancing Numbers and t-Cobalancers

Erdem, Alper

In this work, we determined the general terms of all t-cobalancers, t-cobalancing numbers and Lucas t-cobalancing numbers by solving the Pell equation 2x^2-y^2=2t^2-1 for some integer t \geq 1.

170073

On Filter Convergence and Its Applications to Convergence Theorems

Erdem, Alper | Tunç, Tuncay

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167038

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.

Makale2021Miskolc Mathematical Notes 56 | 0 Erişime Açık
167588

Lineer Cebir Video Ders Notları

Erdem, Alper

Bu kitap, YouTube’da 5 milyon izlenmeyi aşan Sürekli Matematik kanalında yayınlanan “Lineer Cebir” video serisinin detaylı ders notlarını içermektedir. Lineer cebir konusunu anlamak ve pratik yapmak isteyen öğrenciler için bir kaynaktır. Adım adım açıklamalar, çözüm teknikleri ve örneklerle dolu bu notlar; okuyucunun konuya hakimiyetini artırmayı hedeflemektedir. Notlar, video ders notu şeklinde hazırlanmıştır. Videolarda çözümü yapılan bölümler yerine gri dikdörtgenler çizilerek okuyucunun video dersleri dinlerken tamamlaması için boş bırakılmıştır.

167043

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.