On boundedly-convex functions on pseudo-topological vector spaces
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-...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200000727 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849308934584664064 |
|---|---|
| author | Vladimir Averbuch |
| author_facet | Vladimir Averbuch |
| author_sort | Vladimir Averbuch |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0b987f9ee4364701992b58f084ef5d26 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0b987f9ee4364701992b58f084ef5d262025-08-20T03:54:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0123214115110.1155/S0161171200000727On boundedly-convex functions on pseudo-topological vector spacesVladimir Averbuch0Silesian University, Bezručovo nám. 13, Opava 74601, Czech RepublicNotions 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.http://dx.doi.org/10.1155/S0161171200000727Filterpseudo-topologyconvergence space pseudo-topologizerpseudo-topological vector space boundedly-convexLipschitz-continuous. |
| spellingShingle | Vladimir Averbuch On boundedly-convex functions on pseudo-topological vector spaces International Journal of Mathematics and Mathematical Sciences Filter pseudo-topology convergence space pseudo-topologizer pseudo-topological vector space boundedly-convex Lipschitz-continuous. |
| title | On boundedly-convex functions on pseudo-topological vector spaces |
| title_full | On boundedly-convex functions on pseudo-topological vector spaces |
| title_fullStr | On boundedly-convex functions on pseudo-topological vector spaces |
| title_full_unstemmed | On boundedly-convex functions on pseudo-topological vector spaces |
| title_short | On boundedly-convex functions on pseudo-topological vector spaces |
| title_sort | on boundedly convex functions on pseudo topological vector spaces |
| topic | Filter pseudo-topology convergence space pseudo-topologizer pseudo-topological vector space boundedly-convex Lipschitz-continuous. |
| url | http://dx.doi.org/10.1155/S0161171200000727 |
| work_keys_str_mv | AT vladimiraverbuch onboundedlyconvexfunctionsonpseudotopologicalvectorspaces |