Quantitative Bounds for Positive Solutions of a Stević Difference Equation

Abstract

This paper studies the behavior of positive solutions to the following particular case of a difference equation by Stević xn+1=A+xnp/xn−kpk+1, n∈ℕ0, where A,p∈(0,+∞), k∈ℕ, and presents theoretically computable explicit lower and upper bounds for the positive solutions to this equation. Besides, a concrete example is given to show the computing approaches which are effective for small parameters. Some analogous results are also established for the corresponding Stević max-type difference equation.