A parametric kind of Fubini-Fibonacci polynomials and their generalizations
Résumé
In this paper, we introduce bivariate kind of three-variable Fubini-Fibonacci polynomials and their associated numbers within the approach of Golden F- Calculus. Utilizing generating functions, we derive several fundamental properties, including summation theorems, recurrence relations, symmetry properties, and F-derivative identities. We further establish connections with, Bernoulli-Fibonacci, Euler-Fibonacci, Genocchi-Fibonacci Stirling-Fibonacci numbers of the second kind and present mu,ltiple summation formulas and convolution-type identities. The proposed approach enriches the theory of Fibonacci-based special polynomials and opens new avenues for applications in combinatorics, number theory, approximation theory, and matrix analysis.
Téléchargements
Références
A. Aledamat, W. A. Khan, U. Duran, C. S. Ryoo, Construction for q-hypergeometric Bernoulli polynomials of a complex variable with applications computer modeling. Advanced Mathematical Models and Applications, 9(1) (2024), 68-92.
M. S. Alatawi, W. A. Khan, C. Kızılates, C. S. Ryoo, Some Properties of Generalized Apostol-Type Frobenius-EulerFibonacci Polynomials. Mathematics. 2024; 12(6):800.
A. Z. Border, The r-Stirling numbers. Disc. Math. (1984), 49(3), 241-259.
Z. Chen, N. Omur, S. Koparal, W. A. Khan, Some identities with multi generalized q-hyper harmonic numbers of order r. Symmetry, (2023), 15:917, 1-10.
H. Guan, N. Omur, S. Koparal, W. A. Khan, q-analogue of Hn,m and their applications. Mathematics, (2023), 15:943, 1-10.
H. Guan H, W. A. Khan, C. Kızılates, C. S. Ryoo, On Certain Properties of Parametric Kinds of Apostol-Type Frobenius-Euler-Fibonacci Polynomials. Axioms. 2024; 13(6):348.
M. Fadel, M. S. Alatawi, W. A. Khan, Two variable q-Hermite based Applell polynomials and their applications. Mathematics, (2024), 12:1358, 1-17.
W. A. Khan, M. S Alatawi, C. S. Ryoo, U. Duran, Novel properties of q-Sine based and q-Cosine-based q-Fubini polynomials. Symmetry, (2023), 15:356, 1-18.
W. A. Khan, A note on q-analogue of degenerate Catalan numbers associated p-adic integral on Zp. Symmetry Journal. 14(119) (2022), 1-10. doi.org/10.3390/sym14061119.
W. A. Khan, A note on q-analogues of degenerate Catalan-Daehee numbers and polynomials. Journal of Mathematics, (2022), Article ID 9486880, 9 pages https://doi.org/10.1155/2022/9486880.
O. K. Pashaev, S. Nalci, Golden quantum oscillator and Binet–Fibonacci calculus. J. Phys A: Math. Theor. 2012;45:23 pp.
O. K. Pashaev, Quantum calculus of Fibonacci divisors and infinite hierarchy of bosonic-fermionic golden quantum oscillators. Internat. J. Geom. Methods Modern Phys. 2021;18:32 pp.
E. Krot E, An introduction to finite fibonomial calculus. Centr.Eur.J.Math. 2004;2:754-766.
M. Ozvatan, Generalized golden-Fibonacci calculus and applications. Ph.D. thesis, Izmir Institute of Technology 2018.
S. Kus, N. Tuglu, T. Kim, Bernoulli F -polynomials and Fibo-Bernoulli matrices. Adv. Differ. Equ. 2019;2019:145.
O. K. Pashaev, M. Ozvatan M. Bernoulli-Fibonacci Polynomials. arXiv preprint. 2020. arXiv:2010.15080.
N. Tuglu, E. Ercan, Some properties of Apostol Bernoulli Fibonacci and Apostol Euler Fibonacci Polynomials. Icmee-2021, 32-34.
E. Gulal, N. Tuglu, Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions. TJMCS. 2023;15(1): 203-211.
C. Kızılates, H. Ozturk, On parametric types of Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials via Golden calculus. AIMS Mathematics. 2023, 8(4): 8386-8402.
L. Kargın, Some Formulae for Products of Geometric Polynomials with Applications. J. Integer Seq. 2017;20:1-15.
S. M. Tanny. On some numbers related to the Bell numbers. Canad. Math. Bull. 1974/75;17(5):733–738.
N. Kılar, Y. Simsek, A new family of Fubini type numbers and polynomials associated with Apostol- Bernoulli numbers and polynomials. J. Korean Math. Soc. 2017;54: 1605-1621.
H. M. Srivastava, C. Kizilates, A parametric kind of the Fubini-type polynomials. Rev R Acad Cienc Exactas Fıs Nat Ser A Mat (RACSAM). 2019;113:3253-3267.
Y. Rao, W. A. Khan, S. Araci, C. S. Ryoo, Explicit properties of Apostol-type Frobenius-Euler polynomials involving q-trigonometric function with applications in computer modeling. Mathematics, (2023), 11:2386, 1-21.
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
