Integral of an extension of the sine addition formula

: pp. 833–840
Received: February 18, 2023
Accepted: July 20, 2023
LMIMA Laboratory, Faculty of Sciences and Technology, Moulay Ismail University of Meknès, Morocco

In this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law $\int_{G}f(xyt)d\mu(t)=f(x)\chi_1(y)+\chi_2(x)f(y)$, $x,y\in G$, where $f\colon G\rightarrow \mathbb{C}$, $G$ is a locally compact Hausdorff group, $\mu$ is a regular, compactly supported, complex-valued Borel measure on $G$ and $\chi_1$, $\chi_2$ are fixed characters on $G$.

  1. Stetkær H.  Functional equations on groups.  World Scientific Publishing Company, Singapore (2013).
  2. Aczél J.  Lectures on Functional Equations and Their Applications.  Mathematics in Science and Engineering, vol. 19. Academic Press, New York (1966).
  3. Kannappan P.  Functional Equations and Inequalities with Applications.  Springer, New York (2009).
  4. Székelyhidi L.  Convolution Type Functional Equations on Topological Abelian Groups.  Series on Soviet and East European Mathematics.  World Scientific Publishing Company (1991).
  5. Chung J. K., Kannappan Pl., Ng C. T.  A generalization of the cosine-sine functional equation on groups.  Linear Algebra and its Applications.  66, 259–277 (1985).
  6. Poulsen Th. A., Stetkær H.  On the trigonometric subtraction and addition formulas.  Aequationes Mathematicae.  59, 84–92 (2000).
  7. Kabbaj S., Tial M., Zeglami D.  The integral cosine addition and sine subtraction laws.  Results in Mathematics.  73, 97 (2018).
  8. Zeglami D., Tial M., Kabbaj S.  The integral sine addition law.  Proyecciones.  38 (2), 203–219 (2019).
  9. Stetkær H.  Extensions of the sine addition law on groups.  Aequationes Mathematicae.  93, 467–484 (2019).
  10. Ebanks B.  Around the Sine Addition Law and d'Alembert's Equation on Semigroups.  Results in Mathematics.  77, 11 (2022).
  11. Stetkær H.  The cosine addition law with an additional term.  Aequationes Mathematicae.  90, 1147–1168 (2016).
  12. Stetkær H.  Trigonometric Functional equations of rectangular type.  Aequationes Mathematicae.  56, 251–270 (1998).
Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 833–840 (2023)