We introduce a generalized convolution product $(F*G)_{\vec\alpha,\vec\beta}$ for integral transform ${\mathcal F}_{\gamma,\eta}$ for functionals defined on $K[0,T]$, the space of complex valued continuous functions on $[0,T]$ that vanish at zero. We study some interesting properties of our generalized convolution product and establish various relationships that exist among the generalized convolution product, the integral transform, and the first variation for functionals defined on $K[0,T]$. We also discuss the associativity of the generalized convolution product.