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A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms Cover

A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms

Open Access
|Mar 2022

References

  1. [1] J. Aczél and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, New York, 1989.10.1017/CBO9781139086578
  2. [2] M. Ayoubi and D. Zeglami, D’Alembert’s functional equations on monoids with an anti-endomorphism, Results Math. 75 (2020), no. 2, Paper No. 74, 12 pp.10.1007/s00025-020-01199-z
  3. [3] A.L. Cauchy, Cours d’Analyse de L’École Royale Polytechnique. Première Partie: Analyse Algébrique, De L’Imprimerie Royale, Paris, 1821.
  4. [4] A. Chahbi, B. Fadli, and S. Kabbaj, A generalization of the symmetrized multiplicative Cauchy equation, Acta Math. Hungar. 149 (2016), no. 1, 170–176.
  5. [5] J. d’Alembert, Addition au Mémoire sur la courbe que forme une corde tendue mise en vibration, Hist. Acad. Berlin 1750 (1750), 355–360.
  6. [6] B. Ebanks and H. Stetkær, d’Alembert’s other functional equation on monoids with an involution, Aequationes Math. 89 (2015), no. 1, 187–206.
  7. [7] B. Fadli, S. Kabbaj, K.H. Sabour, and D. Zeglami, Functional equations on semigroups with an endomorphism, Acta Math. Hungar. 150 (2016), no. 2, 363–371.
  8. [8] B. Fadli, D. Zeglami, and S. Kabbaj, A joint generalization of Van Vleck’s and Kannappan’s equations on groups, Adv. Pure Appl. Math. 6 (2015), no. 3, 179–188.
  9. [9] B. Fadli, D. Zeglami, and S. Kabbaj, A variant of Wilson’s functional equation, Publ. Math. Debrecen 87 (2015), no. 3-4, 415–427.
  10. [10] Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer, New York, 2009.10.1007/978-0-387-89492-8
  11. [11] K.H. Sabour, A. Charifi, and S. Kabbaj, On a variant of µ-Wilson’s functional equation with an endomorphism, in: G.A. Anastassiou, J.M. Rassias (eds.), Frontiers in Functional Equations and Analytic Inequalities, Springer, Cham, 2019, pp. 93–111.10.1007/978-3-030-28950-8_5
  12. [12] H. Stetkær, On multiplicative maps, Semigroup Forum 63 (2001), no. 3, 466–468.
  13. [13] H. Stetkær, Functional Equations on Groups, World Scientific Publishing Co., Singapore, 2013.10.1142/8830
  14. [14] H. Stetkær, A variant of d’Alembert’s functional equation, Aequationes Math. 89 (2015), no. 3, 657–662.
  15. [15] D. Zeglami, B. Fadli, and S. Kabbaj, Harmonic analysis and generalized functional equations for the cosine, Adv. Pure Appl. Math. 7 (2016), no. 1, 41–49.
DOI: https://doi.org/10.2478/amsil-2022-0004 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 1 - 14
Submitted on: May 1, 2021
Accepted on: Feb 24, 2022
Published on: Mar 22, 2022
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2022 Ahmed Akkaoui, Mohamed El Fatini, Brahim Fadli, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.