John A. Baker

Pexider's equation and aggregation of allocations

An extension theorem for Pexiders equation is proved and used to generalize the results in [4] to cases with weights with more than one constraint and to more general domains in a form which can be applied to multiobjective linear programming.

A GENERAL FUNCTIONAL EQUATION AND ITS STABILITY

Suppose that V and B are vector spaces over Q, R or C and α 0 , β 0 ,...,α m ,β m are scalar such that α j β k -α k β j ¬= 0 whenever 0 < j < k < m. We prove that if fk: V → B for 0 < k < m and formula math. then each f k is a generalized polynomial map of degree at most m - 1. In case V = R and B = C we show that if some f k is bounded on a set of positive inner Lebesgue measure, then it is a genuine polynomial function. Our main aim is to establish the stability of (*) (in the sense of Ulam) in case B is a Banach space. We also solve a distributional analogue of (*) and prove a mean value theorem concerning harmonic functions in two real variables.

Distributional methods for functional equations

Summary. At the 37th International Symposium on Functional Equations (Huntington, West Virginia, May 16—23, 1999) the author presented a distributional method for solving certain functional equations of the form¶¶

On a functional equation of Aczél and Chung

\sum^N_{k=0}c_k(\xi)f_k(F_k(\xi))=0,\quad \xi\in\Omega

Some propositions related to a dilation theorem of W. Benz

.¶Here

Integration of radial functions

\Omega

Functional Equations and Weierstrass Transforms

is a region (nonempty, open, connected set) in

Functional Equations in Vector Spaces, Part II

{\Bbb R}^{n},\,c_k : \Omega \rightarrow {\Bbb C}

Mappings Whose Derivatives are Isometries

are given

On a functional equation of Luce

C^\infty