Alper Erdem
FEN FAKÜLTESİ MATEMATİK BÖLÜMÜ ANALİZ VE FONKSİYONLAR TEORİSİ ANABİLİM DALI
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Varyant-
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E-Postaalpererdem@mersin.edu.tr
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Web Sitesi
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Durum-
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ÜnvanArş.Gör.
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YÖK Araştırmacı No316329
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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.
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.
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.
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 some semi-convergences with applications on Korovkin-type theorems
Erdem, Alper | Tunç, Tuncay
On some semi-convergences with applications on Korovkin-type theorems
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 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.
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.
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.
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.
On statistically convergence theorems for Lebesgue integrable functions
Erdem, Alper | Tunç, Tuncay
On statistically convergence theorems for Lebesgue integrable functions
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.
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.