Results 71 to 80 of about 14,002 (132)
A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Given a vector space X, we investigate the solutions f:R→X of the linear functional equation of third order f(x) = pf(x − 1) + qf(x − 2) + rf(x − 3), which is strongly associated with a well‐known identity for the Fibonacci numbers. Moreover, we prove the Hyers‐Ulam stability of that equation.
Soon-Mo Jung +2 more
wiley +1 more source
Invertibility and Explicit Inverses of Circulant‐Type Matrices with k‐Fibonacci and k‐Lucas Numbers
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant‐type matrices with the k‐Fibonacci and k‐Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which ...
Zhaolin Jiang +3 more
wiley +1 more source
Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Circulant type matrices have become an important tool in solving differential equations. In this paper, we consider circulant type matrices, including the circulant and left circulant and g‐circulant matrices with the sum and product of Fibonacci and Lucas numbers.
Zhaolin Jiang +3 more
wiley +1 more source
Complex Factorizations of the Lucas Sequences via Matrix Methods
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev polynomials of the second kind. Furthermore, we also obtain the complex factorizations of the second Lucas
Honglin Wu, Mehmet Sezer
wiley +1 more source
Applications and properties of Jacobsthal and Jacobsthal Lucas numbers [PDF]
, 2008 Bu çalışmada, Horadam tarafından tanımlanmış olan Jacobsthal ve Jacobsthal Lucas sayılarının verilen özelliklerine ek olarak bazı özellikler elde edildi. Jacobsthal sayılarının bölünebilme özellikleri verildi.
Köken, Fikri
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Non-Fisherian generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsUsing biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
doaj +1 more source
On Jacobsthal and Jacobsthal-Lucas hybrid numbers [PDF]
, 2018 The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper we consider special kinds of hybrid numbers, namely the Jacobsthal and the Jacobsthal-Lucas hybrid numbers and we give some their ...
Szynal-Liana, Anetta, Włoch, Iwona
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, 2015 Abstract and Applied Analysis, Volume 2015, Issue 1, 2015.
Shurong Sun +3 more
wiley +1 more source
Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials [PDF]
, 2013 In this study we define and study the Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials. We give generating function, Binet formula, explicit formula, Q matrix, determinantal representations and partial derivation of these polynomials.
Gurel, E, Asci, M
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On Generalized Third-Order Jacobsthal Numbers [PDF]
, 2021 In this paper, we investigate the generalized third order Jacobsthal sequences and we deal with, in detail, four special cases, namely, third order Jacobsthal, third order Jacobsthal-Lucas, modified third order Jacobsthal, third order Jacobsthal Perrin ...
Yüksel Soykan, Evren Eyican Polatlı
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