The m-extension of Fibonacci and Lucas p-difference sequences

Abstract

In this paper we define the m−extension of Fibonacci and Lucas p−difference sequences by using the m−extension of Fibonacci and Lucas p−numbers. We investigate some properties of our new sequences and introduce some relations between the m−extension of Fibonacci and Lucas p−difference sequences and the m−extension of Fibonacci and Lucas p−numbers. Moreover, we present the sums and generating function of the m−extension of Fibonacci and Lucas p−difference sequences. Finally, we study the m−extension of Fibonacci p−difference Newton polynomial interpolation.

New families of Horadam numbers associated with finite operators and their applications

“…After Falcon and Catarino 17,18 defined and studied new difference sequences called Pell, k ‐Jacobsthal and k ‐Jacobsthal‐Lucas difference sequences, respectively. Köme and Yazlık 19 defined the m ‐extension of Fibonacci and Lucas p ‐difference sequences by using the m ‐extension of Fibonacci and Lucas p ‐numbers. Then they have investigated some properties of m ‐extension of Fibonacci and Lucas p ‐difference sequences.…”

Asymptotic properties of Kneser type solutions for third order half-linear neutral difference equations

“…Oscillatory and asymptotic properties of solution of equation (1.1) and its special cases have been an active area of investigation in recent years; see for example [2][3][4][5][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references contained therein. The well known discrete version of Kiguradze's theorem [1] can be used to describe the structure of the solution space for the nonoscillatory solutions.…”