Uniformly anti-Schwartz function
by
Kandasamy Muthuvel
University of Wisconsin-Oshkosh

A function f : R --> R is uniformly anti-Schwartz if there exists a positive real number such that for every real number x there exists a positive real number d(x) such that for every real number h with 0 < h < d(x), f(x+h) + f(x-h) - 2f(x). Let f : R --> [0, 1] be a function, S(x) = { h > 0 : f(x+h) = f(x-h) } and T(x) = { h > 0 : f(x+h) = f(x-h) = f(x) }. It is known that 0 is a limit point of S(x) for some x. However it is unknown whether 0 is a limit point of T(x). In this talk we shall discuss some results involving S(x) and T(x).

Date received: July 3, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-80.