Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X2120170101Lipschitz properties of convex functions21494145810.22034/aot.1610.1022ENStefan CobzasBabes-Bolyai University,
Department of MathematicsJournal Article20161003The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $Omega$ of a locally convex space $X$ and taking values in a locally convex space $Y$ ordered by a normal cone.<br />One proves also equi-Lipschitz properties for pointwise bounded families of continuous convex<br />mappings, provided the source space $X$ is barrelled.<br /> Some results on Lipschitz properties of continuous convex functions defined on metrizable topological vector spaces are included as well.<br />The paper has a methodological character - its aim is to show that some geometric properties (monotonicity of the slope, the normality of the seminorms) allow to extend the proofs from the scalar case to the vector one. In this way the proofs become more transparent and natural.http://www.aot-math.org/article_41458_5d243e360281e6cdca04379e93e5493c.pdf