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  • 1 Institute of Mathematics, Silesian University, Bankowa 14, 40–007 Katowice, Poland
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Abstract

We deal with the functional equation
ea
motivated by quadrature rules of approximate integration. In previous results the solutions of this equation were found only in some particular cases. For example the coefficients λi were supposed to be rational or the equation in question was solved only for n=2. In the current paper we do not assume any particular form of coefficients occurring in this equation and we allow n to be any positive integer. Moreover, we obtain a solution of our equation without any regularity assumptions concerning the functions f and F.
  • [1] Bessenyei, M., Páles, Zs. 2010 Characterization of higher order monotonicity via integral inequalities Proc. Roy. Soc. Edinburgh Sect. A 140 723736 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [2] Ger, J. 2002 On Sahoo-Riedel equations on a real interval Aequationes Math. 63 168179 .

  • [3] Haruki, Sh. 1979 A property of quadratic polynomials Amer. Math. Monthly 86 577579 .

  • [4] Kannappan, Pl. 2003 Rudin’s problem on groups and a generalization of mean value theorem Aequationes Math. 65 8292.

  • [5] Kannappan, Pl., Sahoo, P. K., Jacobson, M. S. 1995 A characterization of low degree polynomials Demonstratio Math. 28 8796.

  • [6] Koclȩga-Kulpa, B., Szostok, T. 2008 On some equations connected to Hadamard inequalities Aequationes Math. 75 119129 .

  • [7] Koclȩga-Kulpa, B., Szostok, T. 2008 On a functional equation connected to Gauss quadrature rule Ann. Math. Sil. 22 2740.

  • [8] Koclȩga-Kulpa, B., Szostok, T., Wa̧sowicz, Sz. 2009 On functional equations connected to quadrature rules Georgian Math. J. 16 725736.

    • Search Google Scholar
    • Export Citation
  • [9] Koclȩga-Kulpa, B., Szostok, T., Wa̧sowicz, Sz. 2009 On some equations stemming from quadrature rules Ann. Acad. Pedagog. Crac. Stud. Math. VIII 1930.

    • Search Google Scholar
    • Export Citation
  • [10] Koclȩga-Kulpa, B., Szostok, T., Wa̧sowicz, Sz. 2009 Some functional equations characterizing polynomials Tatra Mt. Math. Publ. 44 2740.

    • Search Google Scholar
    • Export Citation
  • [11] Páles, Zs. 2008 On functional equations characterizing polynomials Acta Sci. Math. (Szeged) 74 581592.

  • [12] Sablik, M. 2000 Taylor’s theorem and functional equations Aequationes Math. 60 258267 .

  • [13] Sablik, M., On a problem of P. K. Sahoo – joint work with Arkadiusz Lisak, talk at the 7th KDWS (Bȩdlewo, Poland), January 31–February 3, 2007.

    • Search Google Scholar
    • Export Citation
  • [14] Sahoo, P. K., On a functional equation associated with the trapezoidal rule, talk at the 44th ISFE (Louisville, Kentucky, USA), May 14–20, 2006.

    • Search Google Scholar
    • Export Citation
  • [15] Riedel, T., Sahoo, P. K. 1998 Mean Value Theorems and Functional Equations World Scientific Singapore–New Jersey–London–Hong Kong.

    • Search Google Scholar
    • Export Citation
  • [16] Rudin, W. 1989 Problem E3338 Amer. Math. Monthly 96 641 .

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
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Address
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Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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