(Springer, 2012) Han, Jeong Soon; Kim, Hee Sik; Neggers, Joseph; Hanyang University; University of Alabama Tuscaloosa
In this article, we consider several properties of Fibonacci sequences in arbitrary groupoids (i.e., binary systems). Such sequences can be defined in a left-hand way and a right-hand way. Thus, it becomes a question of interest to decide when these two ways are equivalent, i.e., when they produce the same sequence for the same inputs. The problem has a simple solution when the groupoid is flexible. The Fibonacci sequences for several groupoids and for the class of groups as special cases are also discussed. 2000 Mathematics Subject Classification: 20N02; 11B39.
(Springer, 2012) Han, Jeong Soon; Kim, Hee Sik; Neggers, Joseph; Hanyang University; University of Alabama Tuscaloosa
In this paper we consider Fibonacci functions on the real numbers R, i.e., functions f : R -> R such that for all x is an element of R, f(x + 2) = f(x + 1) + f(x). We develop the notion of Fibonacci functions using the concept of f f-even and f-odd functions. Moreover, we show that if f is a Fibonacci function then lim(x ->infinity) f(x+1)/f(x) = 1+root 5/2.