This paper contains the solution of a functional equation which is a generalization of a functional equation arising in a characterezation of directed divergence and inaccuracy.
Huang, C. F., & Huang, K. N. (2004). Generalized Master Equations with Nonhermitian Operators. Chinese Journal of Physics, 42(3), 221-233. https://www.airitilibrary.com/Article/Detail?DocID=05779073-200406-201210090009-201210090009-221-233