Hyers-Ulam stability of Pielou logistic difference equation

Volume 10, Issue 6, pp 3115--3122 http://dx.doi.org/10.22436/jnsa.010.06.26

Publication Date: June 25, 2017 Submission Date: February 18, 2017

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Authors

Soon-Mo Jung - Mathematics Section, College of Science and Technology, Hongik University, 30016 Sejong, Republic of Korea. Young Woo Nam - Mathematics Section, College of Science and Technology, Hongik University, 30016 Sejong, Republic of Korea.

Abstract

We investigate Hyers-Ulam stability of the first order difference equation \(x_{i+1}=\frac{ax_i+b}{cx_i+d}\) , where \(ad - bc = 1, c \neq 0\) and \(|a+d|>2\). It has Hyers-Ulam stability if the initial point \(x_0\) lies in some definite interval of \(\mathbb{R}\). The condition \(|a+d|>2\) implies that the above recurrence is a natural generalization of Pielou logistic difference equation.

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Keywords

• Hyers-Ulam stability
• Pielou logistic difference equation
• first order difference equation
• linear fractional map
• Verhulst-Pearl differential equation.

MSC

•  39A30
•  39B82

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