Exploring the stability of two different forms of a same functional equation

Within this manuscript, we shall delve into the direct method and explore the general solution as well as the classical stability of the ensuing reciprocal functional equation [f(x-y+z)-f(3x+y-z)][f(x+y-z)+2f(x-y+z)]-2f(x-y+z)^2=0 in Banach spaces. Moreover, another objective of this work is to obtain another interesting result of stability of the same equation but this time, we make a little change of the above equation and we obtain a new stability result however with a supplementary condition on the mapping f.