On certain functional derivatives

The functional derivative J_y =F_y – (d/dx)F_y of the functionalJ[y] = _a^bF(x,y,y)dx may be computed by the limitJ_y(x) = lim ₀(J/), where is the area under a positive local variation atx, provided the height of the variation vanishes faster than the square of its width. This justifies the use of this limit by Gelfand and Fomin (Ref. 1).This work was supported in part by The National Research Council of Canada, Grant No. A-8744. The author would like to thank Dr. F. H. Hsu for discussions.