Superstability of Pexiderized functional equations arising from distance measures

作者：Kim Gwang Hui; Lee Young Whan^*

来源：Journal of Nonlinear Sciences and Applications, 2016, 9(2): 413-423.

DOI：10.22436/jnsa.009.02.07

• Distance measure
• superstability
• multiplicative function
• stability of functional equation

In this paper, we obtain the superstability of the functional equation
f (pr, qs) + g(ps, qr) = theta (pq, rs)h(p, q)k(r, s)
for all p, q, r, s is an element of G, where G is an Abelian group, f, g, h, k are functionals on G(2), and theta is a cocycle on G(2). This functional equation is a generalized form of the functional equation f (pr, qs) + f (ps, qr) = f (p, q) f (r, s), which arises in the characterization of symmetrically compositive sum-form distance measures and the information measures, and also they can be represented as products of some multiplicative functions and the exponential functional equations. As corollaries, we obtain the superstability of the many functional equations (combination of three variables functions, for example: f (pr, qs) + g(ps, qr) = theta (pq, rs)h(p, q)g(r, s)).

• 出版日期2016