We use a generalized Brownian motion process to define the generalized Fourier-Feynman transform, the convolution product, and the first variation. We then examine the various relationships that exist among the first variation, the generalized Fourier-Feynman transform, and the convolution product for functionals on function space that belong to a Banach algebra S ( L a b [ 0 , T ] ) . These results subsume similar known results obtained by Park, Skoug, and Storvick (1998) for the standard Wiener process.