Results 81 to 90 of about 903 (200)

Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers

Journal of Mathematics, 2023
In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
doaj   +1 more source

The sequences of Fibonacci and Lucas for quadratic fields

Boletim da Sociedade Paranaense de Matemática
We construct the sequences of Fibonacci and Lucas in any quadratic field $\mathbb{Q}(\sqrt{d}\,)$ with $d>0$ square free, noting that the general properties remain valid as those given by the classical sequences of Fibonacci and Lucas for the case $d = 5$, under the respective variants.
Pablo Lam-Estrada, Myrian Rosalia Maldonado-Ramirez, Jose Luis Lopez-Bonilla, Fausto Jarquin Zarate, R. Rajendra, Siva Kota Reddy Polaepalli   +5 more
openaire   +1 more source

Coefficient Bounds and Fekete–Szegö Inequalities for a New Family of Bi‐Univalent Functions Associated With Horadam Polynomial

Journal of Mathematics, Volume 2026, Issue 1, 2026.
We define in this paper a new class of normalized bi‐univalent functions through Horadam polynomials. The main aim of this paper is to provide sharp estimates for the second and third Taylor–Maclaurin coefficients of functions in this new class. We also obtain the Fekete–Szegö inequality for these functions.
Musthafa Ibrahim, Jihad Younis, Ali N. A. Koam, Mohammad Uzair Shah, Smritijit Sen   +4 more
wiley   +1 more source

Fibonacci and Lucas matrix sequences and their properties [PDF]

, 2009
Bu çalışmada, Fibonacci ve Lucas matris dizileri tanımlanmıştır ve Fibonacci matris dizisinin genelleştirilmiş Fibonacci sayı dizisi ile; Lucas matris dizisinin de genelleştirilmiş Lucas sayı dizisi ile olan ilişkileri elde edilmiştir.Fibonacci ve Lucas ...
Civciv, Hacı
core  

Properties of Generalized Bronze Fibonacci Sequences and Their Hyperbolic Quaternions

Axioms
In this study, we establish some properties of Bronze Fibonacci and Bronze Lucas sequences. Then we find the relationships between the roots of the characteristic equation of these sequences with these sequences.
Engin Özkan, Hakan Akkuş, Alkan Özkan
doaj   +1 more source

A Note on Stability of a Linear Functional Equation of Second Order Connected with the Fibonacci Numbers and Lucas Sequences

Journal of Inequalities and Applications, 2010
We prove the Hyers-Ulam stability of a second-order linear functional equation in single variable (with constant coefficients) that is connected with the Fibonacci numbers and Lucas sequences.
Janusz Brzdęk, Soon-Mo Jung
doaj   +2 more sources

Narayana Numbers With Zeckendorf Partition in Two Terms

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The Narayan’s cow sequence starts with the terms 1, 1, and 1. Each subsequent term is obtained as the sum of the previous term and the term three places before. A term of this sequence is called a Narayana number. The mathematician Zeckendorf proved that every positive integer has a unique decomposition into a sum of distinct and nonconsecutive ...
Japhet Odjoumani, Salifou Nikiema, Shikha Binwal   +2 more
wiley   +1 more source

Fibonacci Cartan and Lucas Cartan numbers

Open Mathematics
This study introduces Fibonacci Cartan and Lucas Cartan numbers, extending the classical Fibonacci and Lucas sequences into the framework of Cartan numbers.
Öztürk İskender, Çakır Hasan
doaj   +1 more source

Bi‐Starlike Function of Complex Order Involving Rabotnov Function Associated With Telephone Numbers

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Telephone numbers defined through the recurrence relation Qn=Qn−1+n−1Qn−2 for n ≥ 2, with initial values of Q0=Q1=1. The study of such numbers has led to the establishment of various classes of analytic functions associated with them. In this paper, we establish two new subclasses of bi‐convex and bi‐starlike functions of complex order in the open unit
Sa’ud Al-Sa’di, Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Ming-Sheng Liu   +3 more
wiley   +1 more source

On the Existence of Solutions of Diophantine Equations Related to Subbalancing Numbers

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, we introduce a new sequence of subbalancing numbers by considering balancing numbers as the values of D in the Diophantine equations provided by subbalancing numbers. For this, first we prove that when the values of the positive integer D are chosen as balancing numbers, there exist integer solutions of the Diophantine equations that ...
Selin Sarı, Gül Karadeniz-Gözeri, Pramita Mishra   +2 more
wiley   +1 more source