ON FUNCTIONAL EQUATIONS CONNECTED WITH QUADRATURE RULES

被引：0
作者：
Koclega-Kulpa, Barbara [1 ]
Szostok, Tomasz [1 ]
Wasowicz, Szymon [2 ]
机构：
[1] Silesian Univ, Inst Math, PL-40007 Katowice, Poland
[2] Univ Bielsko Biala, Dept Math & Comp Sci, PL-43309 Bielsko Biala, Poland
来源：
GEORGIAN MATHEMATICAL JOURNAL | 2009年 / 16卷 / 04期
关键词：
Approximate integration; functional equations; polynomial functions; quadrature rules;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The functional equations of the form F(y) - F(x) = (y-x)[alpha(0)f(x) + Sigma(n)(k=1)alpha(k)f(lambda(k)x + (1 - lambda(k))y) + alpha(n+1)f(y)] are considered. They are connected with quadrature rules of the approximate integration. We show that such equations characterize polynomials in the class of continuous functions. It is also shown that if the number of components is sufficiently small, then the continuity is forced by the equation itself. Unique solvability of the considered problem are established.
引用
收藏
页码：725 / 736
页数：12
相关论文
共 50 条
  • [1] On a functional equation connected to Hermite quadrature rule
    Koclega-Kulpa, Barbara
    Szostok, Tomasz
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 414 (02) : 632 - 640
  • [2] ON A CLASS OF EQUATIONS STEMMING FROM VARIOUS QUADRATURE RULES
    Koclega-Kulpa, B.
    Szostok, T.
    ACTA MATHEMATICA HUNGARICA, 2011, 130 (04) : 340 - 348
  • [3] Exponential Quadrature Rules for Linear Fractional Differential Equations
    Roberto Garrappa
    Marina Popolizio
    Mediterranean Journal of Mathematics, 2015, 12 : 219 - 244
  • [4] On a class of equations stemming from various quadrature rules
    B. Koclȩga-Kulpa
    T. Szostok
    Acta Mathematica Hungarica, 2011, 130 : 340 - 348
  • [5] Exponential Quadrature Rules for Linear Fractional Differential Equations
    Garrappa, Roberto
    Popolizio, Marina
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2015, 12 (01) : 219 - 244
  • [6] On quadrature rules for solving Partial Differential Equations using Neural Networks
    Rivera, Jon A.
    Taylor, Jamie M.
    Omella, Angel J.
    Pardo, David
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 393
  • [7] Preconditioners for Wiener-Hopf equations with high-order quadrature rules
    Lin, FR
    Ng, MK
    Chan, RH
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (04) : 1418 - 1431
  • [8] A probabilistic model for quadrature rules
    Masjed-Jamei, Mohammad
    Dehghan, Mehdi
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 187 (02) : 1520 - 1526
  • [9] Quadrature rules from a RII type recurrence relation and associated quadrature rules on the unit circle
    Cleonice F. Bracciali
    Junior A. Pereira
    A. Sri Ranga
    Numerical Algorithms, 2020, 83 : 1029 - 1061
  • [10] Quadrature rules from a RII type recurrence relation and associated quadrature rules on the unit circle
    Bracciali, Cleonice F.
    Pereira, Junior A.
    Ranga, A. Sri
    NUMERICAL ALGORITHMS, 2020, 83 (03) : 1029 - 1061
12345