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1. Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties

Author

Özat, Zeynep, Çekim, Bayram, Kızılateş, Can, and Qi, Feng

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Combinatorics, 41A58 (Primary), 11B73, 11B83, 26A24, 33B10 (Secondary)
Abstract

The purpose of this paper is to define generalized Apostol--Bernoulli polynomials with including a new cosine and sine parametric type of generating function using the quasi-monomiality properties and trigonometric functions. In this study, the Apostol-Bernoulli polynomials with three variable are defined with two new generating functions cosine and sine parameters. Then, we investigate multiplicative and derivative operators, diffrential equations, some summation formulas and partial differential equations for these polynomials. Moreover, we introduce Gould--Hopper--Apostol--Bernoulli type polynomials, Hermite--Appell--Apostol--Bernoulli type polynomials and truncated exponential Apostol--Bernoulli type polynomials. Finally, the special cases of these new polynomials are investigated, and the corresponding results are expressed., Comment: 16 pages

Published
2021

5. On the Harmonic and Hyperharmonic Fibonacci Numbers

Author

Tuglu, Naim, Kızılateş, Can, and Kesim, Seyhun

Subjects
Mathematics - Number Theory, 11B39, 05A19. 05A10, 15A60
Abstract

In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which is finite sums of reciprocals of Fibonacci numbers. We obtain spectral and Euclidean norms of circulant matrices involving harmonic and hyperharmonic Fibonacci numbers.

Published
2015
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18. Harmonik ve hiperharmonik Fibonacci sayıları ve uygulamaları

Author

Kizilateş, Can, Kesim, Seyhun, Tuğlu, Naim, and Matematik Ana Bilim Dalı

Subjects
Matematik, Mathematics
Abstract

Bu tezde, harmonik Fibonacci ve hiperharmonik Fibonacci sayıları tanımlanmıştır. Fark operatör yöntemi kullanılarak harmonik Fibonacci sayılarını içeren çeşitli toplam formülleri elde edilmiştir. Hiperharmonik Fibonacci sayıları için toplamsal özdeşlikler verilmiştir. Elemanları harmonik Fibonacci ve hiperharmonik Fibonacci olan circulant ve r-circulant matrislerin Euclidean ve spektral normları hesaplanmış ve bu normlar için bazı nümerik sonuçlar bulunmuştur. In this thesis, harmonic Fibonacci and hyperharmonic Fibonacci numbers are defined. Several sum formulas for the harmonic Fibonacci numbers are obtained by using the difference operator method. Additive identities of the hyperharmonic Fibonacci numbers are given. Euclidean and spectral norms of circulant and r-circulant matrices with the harmonic Fibonacci and hyperharmonic Fibonacci numbers are calculated and some numerical results are found for these matrix norms. 61

Published
2016

24. On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number.

Author

KIZILATEŞ, Can and TUGLU, Naim

Subjects
*CIRCULANT matrices, *COMPLEX numbers, *CODING theory, *FIBONACCI sequence, *GENERALIZATION
Abstract

In this paper, we study the spectral norms of the geometric circulant matrices Tr* = Circr*(T0.T1, ... Tn-1) and the symmetric geometric circulant matrices STr* = SCircr*), (T0, T1, ... Tn-1), where Tn denotes the nth Tribonacci number and r is any complex number. [ABSTRACT FROM AUTHOR]

Published
2018

25. Gauss binomiyel ve fibonomiyel katsayıların özellikleri

Author

Kizilateş, Can, Tuğlu, Naim, and Matematik Anabilim Dalı

Subjects
Matematik, Mathematics
Abstract

Bu çalışmada Gauss Binomiyel katsayıların ve Fibonomiyel Katsayıların tanımları verildi. Gauss Binomiyel Katsayıların temel özellikleri incelendi. Binomiyel Katsayıları içeren bazı özdeşliklerin q benzerleri verildi. Fibonomiyel Katsayıların temel özellikleri incelendi. Gauss Binomiyel Katsayıların Fibonomiyel Katsayılar cinsinden yazılabileceği ve bazı toplamsal q özdeşliklerin Fibonomiyel Katsayılar cinsinden yazılabileceği gösterildi.Anahtar Kelimeler : Binomiyel katsayılar, Gauss Binomiyel Katsayılar, Fibonomiyel Katsayılar In this thesis, the definitions of Gauss Binomial Coefficients and Fibonomial Coefficients were given. Basic features of Gauss Binomial Coefficients were examined. q synonyms of some identities possessing Binomial Coefficients were given. Basic features of Fibonomial Coefficients were examined. It has been proved that Gauss Binomial Coefficients can be expressed in terms of Fibonomial Coefficients and that certain q identities can be expressed in terms of Fibonomial Coefficients.Key Words :Binomial Coefficients, Gauss Binomial coefficients, Fibonomial Coefficients 60

Published
2012

27. q-GENERALIZATION OF BIPERIODIC FIBONACCI AND LUCAS POLYNOMIALS.

Author

KIZILATEŞ, CAN, FİRENGİZ, MIRAC ÇETİN, and TUGLU, NAIM

Subjects
*FIBONACCI sequence, *GENERALIZATION, *POLYNOMIALS, *INTEGERS, *PROOF theory
Abstract

In this paper, we define q-analogue of the biperiodic Fibonacci and Lucas polynomials. We obtain generating function and several properties of these polynomials. We also define q-analogue of the biperiodic incomplete Fibonacci and Lucas polynomials. We show that these polynomials satisfy nonlinear recurrence relations. Then we prove several summation formulas for the biperiodic incomplete q-Fibonacci and q-Lucas polynomials. [ABSTRACT FROM AUTHOR]

Published
2017

28. BINOMIAL TRANSFORMS OF QUADRAPELL SEQUENCES AND QUADRAPELL MATRIX SEQUENCES.

Author

KIZILATEŞ, CAN, TUGLU, NAIM, and ÇEKİM, BAYRAM

Subjects
*MATHEMATICAL sequences, *BINOMIAL equations, *ALGEBRAIC numbers, *INTEGRAL transforms, *MATHEMATICAL analysis
Abstract

In this paper, we apply the binomial transform to the Quadrapell sequence. We investigate some interesting properties the so-obtained new sequence. Moreover we define the matrix sequence of the Quadrapell numbers. Then, we give properties of these new matrix sequences. Finally, we apply binomial transform to Quadrapell matrix sequence and give some algebraic properties of the new sequence. [ABSTRACT FROM AUTHOR]

Published
2017

29. On the Norms of Some Special Matrices with the Harmonic Fibonacci Numbers.

Author

TUGLU, Naim and KIZILATEŞ, Can

Subjects
*MATRIX norms, *NUMBER theory, *HARMONIC analysis (Mathematics), *FIBONACCI sequence, *CIRCULANT matrices
Abstract

The aim of this paper is to study norms of some circulant matrices and some special matrices, which entries consist of harmonic Fibonacci numbers. [ABSTRACT FROM AUTHOR]

Published
2015

30. Quadra Lucas-Jacobsthal Sayıları Üzerine

Author

KIZILATEŞ, Can

Subjects
Lucas Numbers,Jacobsthal Numbers,Binet’s Formula,Circulant Matrix, Binet formülü,Sirkülant matris,Jacobsthal sayıları,Lucas sayıları
Abstract

Bu makalede, Quadra Lucas-Jacobsthal sayıları tanımlanmış ve bu dizilerin çeşitli özellikleri verilmiştir. Dahası elamanları Quadra Lucas-Jacobsthal sayıları olan sirkülant matrislerin spektral normları elde edilmiştir, In this paper, we define the Quadra Lucas-Jacobsthal numbers and then, we give some properties of this sequence. Moreover, we obtain spectral norms of circulant matrices with Quadra Lucas-Jacobsthal numbers.

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