The principal aim of this paper is to show that weakly cone-convex vector-valued functions, as well as weakly cone-quasiconvex vector-valued functions, can be characterized in terms of usual weakly convexity and weakly quasiconvexity of certain real-valued functions, defined by means of the extreme
Some characterizations of convex functions
β Scribed by Yuan-Chuan Li; Cheh-Chih Yeh
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 679 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
β¦ Synopsis
The main result in this paper is to establish some new characterizations of convex functions, in which we also simplify the proof of the characterizations given by Bessenyei and PΓ‘les.
π SIMILAR VOLUMES
A function defined on a Banach space X is called D-convex if it can be represented as a difference of two continuous convex functions. In this work we study the relationship between some geometrical properties of a Banach space X and the behaviour of the class of all D-convex functions defined on it
## Abstract Let __X__ be a space of homogeneous type. The authors introduce some generalized approximations to the identity (for short, GAI) with optimal decay conditions in the sense that these conditions are the sufficient and necessary conditions for these GAI's to characterize BMO(__X__), the s