In this paper, we introduce the modified generalized Fibonacci and Lucas quaternions. We present the generating functions, the Binet formulas and some significant identities for these quaternions. ...

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 ...