On the golden number and Fibonacci type sequences

The paper presents, among others, the golden number ${\displaystyle \phi }$ as the limit of the quotient of neighboring terms of the Fibonacci and Fibonacci type sequence by means of a fixed point of a mapping of a certain interval with the help of Edelstein's theorem. To demonstrate the equality  , where ${\displaystyle f_n}$ is ${\displaystyle n}$-th Fibonacci number also the formula from Corollary $\text{???}$ has been applied. It was obtained using some relationships between Fibonacci and Lucas numbers, which were previously justified.