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International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 2, Pages 141-151
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.