The q-Fibonacci Hyperbolic Functions

In 2005 Stakhov and Rozin introduced a new class of hyperbolic functions which is called Fibonacci hyperbolic functions. In this paper, we study q-analogue of Fibonacci hyperbolic functions. These functions can be regarded as q extensions of classical hyperbolic functions. We introduce the q-analogue of classical Golden ratio as follow phi(q) = 1+root 1+4q(n-2)/2 n >= 2. Making use of this q-analogue of the Golden ratio, we defined sinF(q)h(x) and cosF(q)h(x) functions. We investigated some properties and gave some relationships between these functions.