References
- Y. Aissi, D. Zeglami, and A. Mouzoun, A quadratic functional equation with involutive automorphisms on semigroups, Bol. Soc. Mat. Mex. (3) 28 (2022), no. 1, Paper No. 19, 13 pp.
- A. Akkaoui, Jensen’s functional equation on semigroups, Acta Math. Hungar. 170 (2023), no. 1, 261–268.
- A. Akkaoui, B. Fadli, and M. El Fatini, The Drygas functional equation on abelian semigroups with endomorphisms, Results Math. 76 (2021), no. 1, Paper No. 42, 13 pp.
- A. Akkaoui, M. El Fatini, and B. Fadli, A variant of d’Alembert’s functional equation on semigroups with endomorphisms, Ann. Math. Sil. 36 (2022), no. 1, 1–14.
- B.R. Ebanks, Some generalized quadratic functional equations on monoids, Aequationes Math. 94 (2020), no. 4, 737–747.
- 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.
- H.H. Elfen, T. Riedel, and P.K. Sahoo, A variant of the quadratic functional equation on groups and an application, Bull. Korean Math. Soc. 54 (2017), no. 6, 2165–2182.
- B. Fadli, A. Chahbi, Iz. El-Fassi, and S. Kabbaj, On Jensen’s and the quadratic functional equations with involutions, Proyecciones 35 (2016), no. 2, 213–223.
- B. Fadli, D. Zeglami, and S. Kabbaj, A variant of the quadratic functional equation on semigroups, Proyecciones 37 (2018), no. 1, 45–55.
- V.A. Faĭziev and P.K. Sahoo, Solution of Whitehead equation on groups, Math. Bohem. 138 (2013), no. 2, 171–180.
- P. de Place Friis and H. Stetkær, On the quadratic functional equation on groups, Publ. Math. Debrecen 69 (2006), no. 1–2, 65–93.
- P. Jordan and J. Von Neumann, On inner products in linear, metric spaces, Ann. of Math. (2) 36 (1935), no. 3, 719–723.
- KH. Sabour and S. Kabbaj, Jensen’s and the quadratic functional equations with an endomorphism, Proyecciones 36 (2017), no. 1, 187–194.
- P. Sinopoulos, Functional equations on semigroups, Aequationes Math. 59 (2000), no. 3, 255–261.
- H. Stetkær, Functional equations on abelian groups with involution, Aequationes Math. 54 (1997), no. 1–2, 144–172.
- H. Stetkær, Functional Equations on Groups, World Scientific Publishing Co. Pte. Ltd., Singapore, 2013.
- H. Stetkær, The kernel of the second order Cauchy difference on semigroups, Aequationes Math. 91 (2017), no. 2, 279–288.