Abstract
Let \((S,+)\) be an abelian semigroup, let \(\sigma \) be an involution of S, let X be a linear space over the field \({\mathbb {K}}\in \{{\mathbb {R}},{\mathbb {C}}\}\) and let \(\mu \),\(\nu \) be linear combinations of Dirac measures. In the present paper, we find the general solution \(f:S\rightarrow X\) of the following functional equation
in terms of additive and bi-additive maps. Many consequences of this result are presented.
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The authors wish to thank the referee for a number of constructive comments which have led to essential improvement of the paper.
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Akkaoui, A., Fatini, M.E., Fadli, B. et al. Nice results about quadratic type functional equations on semigroups. Aequat. Math. 94, 83–96 (2020). https://doi.org/10.1007/s00010-019-00653-w
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DOI: https://doi.org/10.1007/s00010-019-00653-w