Abstract
In this note, we consider the following rational difference equation: x n + 1 = f ( x n − r 1 , … , x n − r k ) g ( x n − m 1 , … , x n − m l ) + 1 f ( x n − r 1 , … , x n − r k ) + g ( x n − m 1 , … , x n − m l ) , n = 0 , 1 , … , where f ∈ C ( ( 0 , + ∞ ) k , ( 0 , + ∞ ) ) and g ∈ C ( ( 0 , + ∞ ) l , ( 0 , + ∞ ) ) with k , l ∈ { 1 , 2 , … } , 0 ⩽ r 1 < ⋯ < r k and 0 ⩽ m 1 < ⋯ < m l , and the initial values are positive real numbers. We give sufficient conditions under which the unique equilibrium x ¯ = 1 of this equation is globally asymptotically stable, which extends and includes corresponding results obtained in the recent literature.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
