Abstract
The main goal of this chapter is to find the solutions (f, g) of the generalized variant of μ-d’Alembert’s functional equation
and μ-Wilson’s functional equation
in the setting of semigroups, monoids, and groups, where φ is an endomorphism not necessarily involutive and μ is a multiplicative function. We prove that their solutions can be expressed in terms of multiplicative and additive functions. Many consequences of these results are presented.
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References
A.L. Cauchy, in Cours d’Analyse de l’ecole Polytechnique. Analyse Algebrique, V., Paris, vol. 1 (1821)
J. d’Alembert, Addition au Mémoire sur la courbe que forme une corde tendue mise en vibration. Hist. Acad. Berlin 1750, 355–360 (1750)
B.R. Ebanks, H. Stetkær, d’Alembert’s other functional equation on monoids with an involution. Aequationes Math. 89, 187–206 (2015)
B.R. Ebanks, H. Stetkær, On Wilson’s functional equations. Aequationes Math. 89(2), 339–354 (2015)
E. Elqorachi, A. Redouani, Solutions and Stability of Variant of Wilson’s Functional Equation (2015). arXiv:1505.06512v1 [math.CA]
B. Fadli, S. Kabbaj, K.H. Sabour, D. Zeglami, Functional equation on semigroups with an endomorphism. Acta Math. Hung. 150(2) (2016). https://doi.org/10.1007/s10474-016-0635-9
P.L. Kannappan, A functional equation for the cosine. Can. Math. Bull. 2, 495–498 (1968)
P.L. Kannappan, Functional Equations and Inequalities with Applications (Springer, New York, 2009)
H. Stetkær, Functional Equations on Groups (World Scientific Publishing Co, Singapore, 2013)
W.H. Wilson, On certain related functional equations. Bull. Am. Math. Soc. 26, 300–312 (1919–1920). Fortschr.: 47, 320 (1919–20)
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Sabour, K.H., Charifi, A., Kabbaj, S. (2019). On a Variant of μ-Wilson’s Functional Equation with an Endomorphism. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_5
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DOI: https://doi.org/10.1007/978-3-030-28950-8_5
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