The variational equality for the functional of the general form

We defined a characteristic that serves as a measure of the difference of two vectors associated with a convex function. In terms of this characteristic we establish the variational equality for the extremals of the functional of general form. We consider the results for the minimal surface equation in Finsler space and give them a geometric interpretation. Corollary of results is the convergence "on average" sequence that minimizes this functional.