Abstract:
Let fp;m be a real valued function on R, p be nonnegative integer, k be a positive integer and m be a
nonnegative real number. For all x 2 R, fp;m(x + (p + 1)k) = mfp;m(x + pk) + fp;m(x), we call this
function m�����extension of Fibonacci p�����function with period k. In this paper, we present basic properties of
m�����extension of Fibonacci p�����functions with period k. Specifying p and m, we obtain Fibonacci (p = 1, m =
1) and Pell (p = 1, m = 2) functions. Furthermore, we de ne m�����extension of odd Fibonacci p�����functions
with period k. Moreover, we analyze some properties by using notion of f�����even and f�����odd functions with
period k. We also demonstrate the products and quotients of these functions and provide new results in the
development of Fibonacci functions with period k.
