Stability properties of functional equations describing the scientific laws

Abstract

Recently several authors have studied functional equations in order to find the general form of scientific laws which are invariant under the so-called “admissible transformations” of the variables (see, e.g., [2, 3, 131). The problem has its origin in the theory of dimensional analysis (see, e.g., [11, 12, 14]), but there are also close connections to economics, production theory, etc. (see [6]). The functional equations considered by the above authors-and solved in special cases-have the form