In this paper we describe the complex-valued solutions defined on a double coset hypergroup of the exponential, additive, and quadratic functional equations. Moreover, the -sine functions on a double coset hypergroup are discussed. The double coset hypergroup we consider is closely related to affine groups and spherical functions on them.
Żywilla Fechner. László Székelyhidi. "Functional equations on double coset hypergroups." Ann. Funct. Anal. 8 (3) 411 - 423, August 2017. https://doi.org/10.1215/20088752-2017-0006