International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 2, Pages 141-151
doi:10.1155/S0161171200000727
On boundedly-convex functions on pseudo-topological vector spaces
Silesian University, Bezručovo nám. 13, Opava 74601, Czech Republic
Received 11 April 1997
Copyright © 2000 Vladimir Averbuch. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Notions of a boundedly convex function and of a
Lipschitz-continuous function are extended to the case of
functions on pseudo-topological vector spaces. It is proved that
for “good” pseudo-topologizers Ψ, any continuous Ψ-boundedly convex function is Ψ-differentiable
and its derivative is Ψ-Lipschitz-continuous. As a corollary,
it is shown that any boundedly convex function is Hyers-Lang
differentiable.