Several Types of q-Differential Equations of Higher Order and Properties of Their Solutions

被引：1
作者：
Ryoo, Cheon-Seoung [1 ]
Kang, Jung-Yoog [2 ]
机构：
[1] Hannam Univ, Dept Math, Daejeon 34430, South Korea
[2] Silla Univ, Dept Math Educ, Pusan 46958, South Korea
来源：
MATHEMATICS | 2022年 / 10卷 / 23期
关键词：
q-derivative; q-numbers; q-sigmoid numbers and polynomials; q-differential equations of higher order; q-sigmoid polynomials; symmetric property; SIGMOID FUNCTION;
D O I：
10.3390/math10234469
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The purpose of this paper is to organize various types of higher order q-differential equations that are connected to q-sigmoid polynomials and obtain certain properties regarding their solutions. Using the properties of q-sigmoid polynomials, we show the symmetric properties of q-differential equations of higher order. Moreover, we derive special properties for the approximate roots of q-sigmoid polynomials which are solutions of higher order q-differential equations.
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页数：14
相关论文
共 24 条
  • [1] Andrews G.E., 1999, ENCY MATH ITS APPL, V71
  • [2] Bangerezako G., 2008, INTRO Q DIFFERENCE E
  • [3] Sigmoidal mixed models for longitudinal data
    Capuano, Ana W.
    Wilson, Robert S.
    Leurgans, Sue E.
    Dawson, Jeffrey D.
    Bennett, David A.
    Hedeker, Donald
    [J]. STATISTICAL METHODS IN MEDICAL RESEARCH, 2018, 27 (03) : 863 - 875
  • [4] The general theory of linear q-difference equations
    Carmichael, RD
    [J]. AMERICAN JOURNAL OF MATHEMATICS, 1912, 34 : 147 - 168
  • [5] A note on the Bernoulli and Euler polynomials
    Cheon, GS
    [J]. APPLIED MATHEMATICS LETTERS, 2003, 16 (03) : 365 - 368
  • [6] Comtet L., 1974, Advanced combinatorics
  • [7] Han J, 1995, LECT NOTES COMPUT SC, V930, P195
  • [8] REPRESENTATION OF FUNCTIONS BY SUPERPOSITIONS OF A STEP OR SIGMOID FUNCTION AND THEIR APPLICATIONS TO NEURAL NETWORK THEORY
    ITO, Y
    [J]. NEURAL NETWORKS, 1991, 4 (03) : 385 - 394
  • [9] q-difference equations.
    Jackson, FH
    [J]. AMERICAN JOURNAL OF MATHEMATICS, 1910, 32 : 305 - 314
  • [10] Jackson H.F., 2013, EARTH ENV SCI T R SO, V46, P253, DOI [10.1017/s0080456800002751, DOI 10.1017/S0080456800002751, 10.1017/S0080456800002751]
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