Fibonacci and Lucas Numbers with Applications

On the <i>k</i> -Lucas Numbers and Lucas Polynomials

“…For example, the ratio of two consecutive numbers converges to the Golden ratio 1 5 2 α + = which was thoroughly interested in [13]. We should recall that, for k∈ ℝ + , prove new results based on our previous ones [4,5,6].…”

Generalized Fibonacci – Lucas sequence its Properties

“…The Fibonacci numbers are perhaps most famous for appearing in the rabbit breeding problem, introduced by Leonardo de Pisa in 1202 in his book called Liber Abaci. As illustrate in the tome by Koshy [5] the Fibonacci and Lucas number are arguable two of the most interesting sequence in all of mathematics. Many identities have been documented in an extensive list that appears in the work of Vajda [12], where they are proved by algebra means, even though combinatorial proof of many of these interesting identities.…”

“…We introduced Generalized Fibonacci-Lucas Sequence and its Properties Fibonacci numbers, Lucas number's and their generalization have many interesting Properties and application to almost every field. The Fibonacci sequence [5] is a sequence of numbers starting with integer 0 and 1, where each next term of the sequence calculated as the sum of the previous two. i.e., F F F n 2 n n-1 n-2 ,    ,and F 0,F 1…”

New Banach Sequence Spaces That Is Defined By The Aid Of Lucas Numbers

“…A -space is a sequence space with a linear topology provided each maps : → ℂ, given as follows (Koshy, 2001), (Vajda, 2008): given as follows (Koshy, 2001), (Vajda, 2008):…”

“…In spite of this relation, they exhibit distinct properties. Some fundamental characteristics of Lucas sequences are given as follows (Koshy, 2001), (Vajda, 2008):…”