Application of Banach contraction principle to approximate the golden number

Abstract

This work is devoted to the application of selected fixed point theorems in the problems of convergence of certain sequences to the golden number. It contains the theorem about the fixed point of so-called ψ-contraction specified on the closed interval <a, b> and the local version of Banach Contraction Principle as a conclusion. It will also be used to approximate the golden number.