A note on the order of polynomial-like iterative equations

• Autorzy: Draga S.

Identyfikatory

DOI

10.14708/cm.v56i2.1436

• Języki publikacji: EN

Abstrakty

EN

We show that, under reasonable assumptions, two negative roots can be eliminated from the characteristic equation of a polynomial-like iterative equation. This result gives a new case where we may lower the order of such an equation.

Słowa kluczowe

EN

continuous solution; iterate; polynomial-like iterative equation; recurrence relation

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: Vol 56, No. 2
• Strony: 243--249
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Draga S.

• Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] S. Draga and J. Morawiec, Reducing the polynomial-like iterative equations order and a generalized Zoltán Boros’ problem, Aequationes Math. 90 (2016), 935-950, DOI 10.1007/s00010-016-0420-4.
• [2] A. J. Jerri, Linear Difference Equations with Discrete Transform Methods, Springer 1996, DOI 10.1007/978-1-4757-5657-9.
• [3] J. Matkowski and W. Zhang, Method of characteristic for functional equations in polynomial form, Acta Math. Sin. 13 (1997), 421-432, DOI 10.1007/BF02560023.
• [4] J. Matkowski and W. Zhang, Characteristic analysis for a polynomial-like iterative equation, Chinese Sci. Bull. 43 (1998), 192-196, DOI 10.1007/BF02898908.
• [5] S. Nabeya, On the functional equation f (p + qx + rf (x)) = a + bx + cf (x), Aequationes Math. 11 (1974), 199-211, DOI 10.1007/BF01834919.
• [6] D. Yang and W. Zhang, Characteristic solutions of polynomial-like iterative equations, Aequationes Math. 67 (2004), 80-105, DOI 10.1007/s00010-003-2708-4.
• [7] P. Zhang and X. Gong, Continuous solutions of 3-order iterative equation of linear dependence, Adv. Difference Equ. 318 (2014), DOI 10.1186/1687-1847-2014-318.
• [8] W. Zhang, B. Xu, and W. Zhang, Global solutions for leading coefficient problem of polynomial-like iterative equations, Results. Math. 63 (2013), 79-93, DOI 10.1007/s00025-011-0162-5.
• [9] W. Zhang and W. Zhang, On continuous solutions of n-th order polynomial-like iterative equations, Publ. Math. Debrecen 76 (2010), 117-134.