Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 463918, 9 pages
http://dx.doi.org/10.1155/2014/463918
Research Article

Solution of Several Functional Equations on Nonunital Semigroups Using Wilson’s Functional Equations with Involution

1Department of Mathematics, Kunsan National University, Gunsan 573-701, Republic of Korea
2Department of Mathematics, University of Louisville, Louisville, KY 40292, USA

Received 23 April 2014; Revised 29 July 2014; Accepted 6 August 2014; Published 27 August 2014

Academic Editor: Alberto Fiorenza

Copyright © 2014 Jaeyoung Chung and Prasanna K. Sahoo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. d'Alembert, “Addition au Mémoire sur la courbe que forme une corde tendue mise en vibration,” Histoire de l'Académie Royale, pp. 355–360, 1750. View at Google Scholar
  2. P. K. Sahoo and Pl. Kannappan, Introduction to Functional Equations, CRC Press, Boca Raton, Fla, USA, 2011. View at MathSciNet
  3. H. Stetkær, Functional Equations on Groups, World Scientific, Singapore, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  4. P. Sinopoulos, “Functional equations on semigroups,” Aequationes Mathematicae, vol. 59, no. 3, pp. 255–261, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. W. H. Wilson, “On certain related functional equations,” Bulletin of the American Mathematical Society, vol. 26, no. 7, pp. 300–312, 1920. View at Publisher · View at Google Scholar · View at MathSciNet
  6. W. H. Wilson, “Two general functional equations,” Bulletin of the American Mathematical Society, vol. 31, no. 7, pp. 330–334, 1925. View at Publisher · View at Google Scholar · View at MathSciNet
  7. S. Kaczmarz, “Sur l'équation fonctionnelle fx+fx+y=ϕyfx+y/2,” Fundamenta Mathematicae, vol. 6, pp. 122–129, 1924. View at Google Scholar
  8. G. van der Lyn, “Sur l'équation fonctionnelle f(x+y)+f(x-y)=2f(x)(y),” Mathematica, vol. 16, pp. 91–96, 1940. View at Google Scholar
  9. I. Fenyö, “Uber eineLösungsmethode gewisser Funktionalgleichungen,” Acta Mathematica Academiae Scientiarum Hungaricae, vol. 7, pp. 383–396, 1956. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. K. Chung, B. R. Ebanks, C. T. Ng, and P. K. Sahoo, “On a quadratic-trigonometric functional equation and some applications,” Transactions of the American Mathematical Society, vol. 347, no. 4, pp. 1131–1161, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Aczél, Lectures on Functional Equations and Their Applications, Dover Publications, New York, NY, USA, 2006.
  12. H. Stetkær, “D'Alembert's and Wilson's functional equations for vector and 2 × 2 matrix valued functions,” Mathematica Scandinavica, vol. 87, no. 1, pp. 115–132, 2000. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. J. Aczél and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, New York, NY, USA, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  14. A. Bahyrycz, “On solutions of the second generalization of d'Alembert's functional equation on a restricted domain,” Applied Mathematics and Computation, vol. 223, pp. 209–215, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. I. Corovei, “The functional equation fxy+fxy1=2fxgy for nilpotent groups,” Mathematica, vol. 22, no. 1, pp. 33–41, 1980. View at Google Scholar · View at MathSciNet
  16. I. Corovei, “Wilson's functional equation on P3-groups,” Aequationes Mathematicae, vol. 61, no. 3, pp. 212–220, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. I. Corovei, “Wilson's functional equation on metabelian groups,” Mathematica, vol. 44, no. 2, pp. 137–146, 2002. View at Google Scholar · View at MathSciNet
  18. P. de Place Friis, “d'Alembert's and Wilson's equations on Lie groups,” Aequationes Mathematicae, vol. 67, no. 1-2, pp. 12–25, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. Z. Fechner, “Wilson's functional equation in Banach algebras,” Acta Scientiarum Mathematicarum, vol. 75, no. 1-2, pp. 131–142, 2009. View at Google Scholar · View at MathSciNet · View at Scopus
  20. Z. Fechner, “Wilson's functional equation in algebras,” Studia Scientiarum Mathematicarum Hungarica, vol. 47, no. 3, pp. 388–400, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. H. Stetkær, “Functional equations on abelian groups with involution,” Aequationes Mathematicae, vol. 54, no. 1-2, pp. 144–172, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  22. T. Riedel and P. K. Sahoo, “On a generalization of a functional equation associated with the distance between the probability distributions,” Publicationes Mathematicae Debrecen, vol. 46, no. 1-2, pp. 125–135, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet