On a new class of hyperbolic functions

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The Golden Shofar (2005, methodology): “Developing the approach stated in [17,18] and using (1) the symmetric hyperbolic Fibonacci functions, which were developed in the article [19], namely: Symmetric hyperbolic Fibonacci sine: sFsðxÞ 1⁄4 a x a x ffiffiffi 5 p : ð2Þ”
The k-Fibonacci hyperbolic functions (2008, background): “Note that sFkh(x) is symmetric with respect to the origin, while the graphic of cFkh(x) presents a symmetry with respect to the axis x ¼� 1 2. By doing a change of variable 2x +1= t in function cFkh, the symmetry is for the new variable t with respect to the axis t =0 . For this reason, from now on,”
The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering (2005, background): “Let us consider so-called symmetric hyperbolic Fibonacci functions introduced in [40]:”