A new generalization of Fibonacci hybrid and Lucas hybrid numbers

In the paper, we define the q-Fibonacci hybrid numbers and the q-Lucas hybrid numbers, respectively. Then, we give some algebraic properties of q-Fibonacci hybrid numbers and the q-Lucas hybrid numbers. © 2019 Elsevier Lt

A parametric kind of the Fubini-type polynomials

By introducing two specific generating functions, we define a kind of parametric Fubini-type polynomials. We investigate some fundamental properties of these parametric-kind Fubini-type polynomials. In particular, we derive the relations between the parametric-kind Fubini-type polynomials and other polynomials including (for example) the parametric-kind Apostol–Bernoulli, the Apostol–Euler and the Apostol–Genocchi polynomials of order ?. Finally, we derive several families of multilinear and multilateral generating functions for the parametric-kind Fubini-type polynomials as well as other polynomials which are considered in this paper. © 2019, The Royal Academy of Sciences, Madrid

On the bounds for the spectral norms of geometric circulant matrices

In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices. © 2016, The Author(s)

On the harmonic and hyperharmonic Fibonacci numbers

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 Fn, which is concerned with finite sums of reciprocals of Fibonacci numbers. We obtain the spectral and Euclidean norms of circulant matrices involving harmonic and hyperharmonic Fibonacci numbers. © 2015, Tuglu et al