On boundedly-convex functions on pseudo-topological vector spaces

Vladimir Averbuch

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-11

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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:793857

DOI: 10.1155/S0161171200000727

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