Conditional equations related to Drygas functional equations

Sadegh Izadi; Sedigheh Jahedi; Mehdi Dehghanian

Published: 2025-10-31

2024

Conditional equations related to Drygas functional equations

Sadegh Izadi

, Sedigheh Jahedi , Mehdi Dehghanian

Abstract

We determine the solutions of the conditional Drygas equation for functions f₁ and f₂ that satisfy (y²+y)f₁(x) = (x²+x)f₂(y) for all (x, y)∈ℝ² under the additional conditions y = x², or y = log(x), x > 0 or y = exp(x).

Keywords:

additive function , derivation , Drygas function , quadratic function

Download files

PDF

Citation rules

Izadi, S., Jahedi, S., & Dehghanian, M. (2025). Conditional equations related to Drygas functional equations. Annales Mathematicae Silesianae. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/22804

Licence

This work is licensed under a Creative Commons Attribution 4.0 International License.

The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.

Similar Articles

Detlef Gronau, Maciej Sablik, A functional equation arising from an asymptotic formula for iterates , Annales Mathematicae Silesianae: Vol. 8 (1994)
Irena Kosi-Ulbl, On a functional equation related to two-sided centralizers , Annales Mathematicae Silesianae: Vol. 32 (2018)
Janusz Morawiec, On bounded solutions of a problem of R. Schilling , Annales Mathematicae Silesianae: Vol. 8 (1994)
Karol Baron, Alice Simon, On approximate solutions of an iterative functional equation , Annales Mathematicae Silesianae: Vol. 8 (1994)
Andrzej Nowak, A note on the Fréchet theorem , Annales Mathematicae Silesianae: Vol. 9 (1995)
Tiziana Cardinali, Some characterizations of functions generating K-Schur concave sums and of K-concave set-valued functions , Annales Mathematicae Silesianae: Vol. 9 (1995)
Irena Rachůnková, Topological degree methods in BVPS with nonlinear conditions , Annales Mathematicae Silesianae: Vol. 10 (1996)
Roman Ger, Justyna Sikorska, On the Cauchy equation on spheres , Annales Mathematicae Silesianae: Vol. 11 (1997)
Martin Himmel, Complementary results to Heuvers’s characterization of logarithmic functions , Annales Mathematicae Silesianae: Vol. 31 (2017)
Krzysztof Kozioł, Mieczysław Kula, Witt rings of infinite algebraic extensions of global fields , Annales Mathematicae Silesianae: Vol. 12 (1998)

<< < 6 7 8 9 10 11 12 13 14 > >>

You may also start an advanced similarity search for this article.

References

J. Aczél, The general solution of two functional equations by reduction to functions additive in two variables and with the aid of Hamel bases, Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II 20 (1965), 65–73.
Google Scholar

J. Aczél and J. Dhombres, Functional Equations in Several Variables, Encyclopedia Math. Appl., 31, Cambridge University Press, Cambridge-New York-New Rochelle-Melbourne-Sydney, 1989.
Google Scholar

M. Amou, Quadratic functions satisfying an additional equation, Acta Math. Hungar. 162 (2020), no. 1, 40–51.
Google Scholar

Z. Boros and P. Erdei, A conditional equation for additive functions, Aequationes Math. 70 (2005), no. 3, 309–313.
Google Scholar

Z. Boros and E. Garda-Mátyás, Conditional equations for quadratic functions, Acta Math. Hungar. 154 (2018), no. 2, 389–401.
Google Scholar

Z. Boros and E. Garda-Mátyás, Quadratic functions fulfilling an additional condition along the hyperbola xy = 1, Aequationes Math. 97 (2023), no. 5–6, 1141–1155.
Google Scholar

J. Brzdęk and A. Mureńko, On a conditional Gołąb-Schinzel equation, Arch. Math. (Basel) 84 (2005), no. 6, 503–511.
Google Scholar

M. Dehghanian, S. Izadi, and S. Jahedi, The solution of Drygas functional equations with additional conditions, Acta Math. Hungar. 174 (2024), no. 2, 510–521.
Google Scholar

H. Drygas, Quasi-inner products and their applications, in: A.K. Gupta (Ed.), Advances in Multivariate Statistical Analysis, D. Reidel Publishing Co., Dordrecht, 1987, pp. 13–30.
Google Scholar

B.R. Ebanks, Pl. Kannappan, and P.K. Sahoo, A common generalization of functional equations characterizing normed and quasi-inner-product spaces, Canad. Math. Bull. 35 (1992), no. 3, 321–327.
Google Scholar

E. Garda-Mátyás, Quadratic functions fulfilling an additional condition along hyperbolas or the unit circle, Aequationes Math. 93 (2019), no. 2, 451–465.
Google Scholar

W.B. Jurkat, On Cauchy’s functional equation, Proc. Amer. Math. Soc. 16 (1965), no. 4, 683–686.
Google Scholar

M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, 2nd ed., Birkhäuser Verlag, Basel, 2009.
Google Scholar

S. Kurepa, The Cauchy functional equation and scalar product in vector spaces, Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II 19 (1964), 23–36.
Google Scholar

A. Nishiyama and S. Horinouchi, On a system of functional equations, Aequationes Math. 1 (1968), 1–5.
Google Scholar

H. Stetkær, The kernel of the second order Cauchy difference on semigroups, Aequationes Math. 91 (2017), no. 2, 279–288.
Google Scholar

Sadegh Izadi

s.izadi@sutech.ac.ir
https://orcid.org/0009-0002-4832-383X

Affiliation:

Department of Mathematics, Shiraz University of Technology Iran, Islamic Republic of

Sedigheh Jahedi

Affiliation:

Department of Mathematics, Shiraz University of Technology Iran, Islamic Republic of

Mehdi Dehghanian

Affiliation:

Department of Mathematics, Sirjan University of Technology Iran, Islamic Republic of

2024
Published: 2024-01-18

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

Licence CC

This work is licensed under a Creative Commons Attribution 4.0 International License.

Submit