In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $cal{F}$($C_{a,b}$[0, T]) and in $cal{F}_{A_1,A_2}$.