Let M be a topological monoid, let \(\psi :M\rightarrow M\) be a continuous anti-homomorphism of M, and let \(\mu :M\rightarrow {\mathbb {C}}\) be a continuous multiplicative function such that \(\mu (x\psi (x))=1\) for all \( x\in M\). We describe, in terms of multiplicative functions, additive functions and characters of 2-dimensional representations of M, the solutions (w, g), where \(w,g:M\rightarrow {\mathbb {C}}\), such that w is central and g is continuous, of the new functional equation

We also treat the equation on compact groups and the special equation (when \( \mu =g=1\)): Jensen’s functional equation.

让中号是拓扑幺，让\（\ PSI：M \ RIGHTARROW中号\）是连续的抗同态中号，并让\（\亩：M \ RIGHTARROW {\ mathbb {C}} \）是连续乘法函数，使得\（\亩（X \ PSI（X））= 1 \）对所有\（以M \ X \） 。我们根据乘积函数，M的二维表示的加法函数和字符描述解（w，  g），其中\（w，g：M \ rightarrow {\ mathbb {C}} \）这样该瓦特是中央和克是连续的，新的函数方程的

我们还处理紧群上的方程和特殊方程（当\（\ mu = g = 1 \）时）：詹森函数方程。