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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: ON NONAUTONOMOUS DISCRETE DYNAMICAL SYSTEMS DRIVEN BY MEANS | ON NONAUTONOMOUS DISCRETE DYNAMICAL SYSTEMS DRIVEN BY MEANS RAGHIB M. ABU-SARIS Received 27 March 2006 Revised 13 June 2006 Accepted 14 June 2006 We investigate the asymptotic behavior of nonautonomous discrete dynamical systems governed by the system of difference equations recursive equations yj n 1 Fj n y n j 1 . k n 0 1 2 . where y n y1 n . yk n e Rk y 0 x and Fj n is a mean of k 2 positive real numbers that is a real-valued function satisfying the internality property min x Fj n x max x . Copyright 2006 Raghib M. Abu-Saris. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In this research we are concerned with the long-term behavior of discrete dynamical systems driven by means namely yj n 1 Fj n y n j 1 . k n 0 1 2 . 1.1 where y n y1 n . yk n y 0 x and for each j Fj n is a mean of k 2 positive real numbers that is a real-valued function satisfying the internality property min x Fj n x max x . 1.2 A mean M is strict if min x max x min x M x max x 1.3 and it is said to be isotone if the functions M x2 . Xk . M x1 . Xk-1 are nondecreasing. There is a sizable number of means in the literature. For example i the weighted arithmetic means A x Yk 1 WjXj Wj 0 k 1 Wj 1 ii the weighted geometric means G x nk 1 X- Vj 0 xkj 1 Vj 1 Hindawi Publishing Corporation Advances in Difference Equations Volume 2006 Article ID 43470 Pages 1-7 DOI 10.1155 ADE 2006 43470 2 Nonautonomous DDS driven by means iii the Holder means Hp x Z 1 wxpV l p 0 Wj 0 s Wj 1 1V th p T ph IÌ1 PT lì P3T1Q ỉ . Í v k p k p - 1 iv te Lemei means Lp X t j 1 X j Z t j 1 X j p 1 and so forth. For more information on means and related results we refer the reader to 2-4 and the references cited therein. The dynamical system described in 1.1 is also known in literature as compounding 3 or iteration 9 of means. Markov chains which are .
