In this chapter we discuss some properties of convex functions connected with their boundedness and continuity. We start with the following Lemma 6.1.1. Let D ⊂ ℝ N be a convex and open set, and let f : D
凸函数关键点整理 Properties of Convex Functions 会飞的羊 致敬人类|努力保持好奇心和求知欲 2 人赞同了该文章 发现了一篇介绍convex function的很好的note,将其中要点记录于此。 https://wiki.math.ntnu.no/_media/tma4180/2016v/note2.pdfwiki.math.ntnu.no/_media/tma4180/2016v/note2.pdf ...
In this paper, we obtain that eachg-convex function is continuous and convex, and we also extend Jia and Peng’s result on the characterization ofg-convex function without the bounded assumption of the value ofgat the origin.
A differential calculus of multifunctions J. Math. Analysis Applic. (1970) A. Lasota et al. Asymptotic behavior for differential equations which cannot be locally linearized J. Diff. Eqns (1971) F.A. Valentine Convex Sets (1964) R.T. Rockafellar Convex Analysis (1970) A. Pliś Uniqueness...
(onthedifferentiabilitya.e.ofLipschitzfunctions),areaandcoareaformulas,theprecisestructureofSobolevandBVfunctions,theprecisestructureofsetsoffiniteperimeter,andAleksandrov'stheorem(onthetwicedifferentiabilitya.e.ofconvexfunctions).Thisrevisededitionincludescountlessimprovementsinnotation,format,andclarityofexposition.Also...
PROPERTIES OF SOME SUBCLASSES OF MULTIVALENT FUNCTIONS ASSOCIATED WITH CLOSE-TO-CONVEX FUNCTIONFor analytic function f(z) normalized with f(0)=0 and f'(0)=1 in the open unit disk U. A newclass of f(z) satisfying some conditions with some complex number andsome real number λ . The aim...
Therefore, many authors were interested in this branch and studied this property on sets, cones, hulls and functions. In this paper, we study a modified concept called fuzzy convexity by introducing the notion of convex. M-convex and quasiconvex fuzzy sets, cones and hulls. Some of their ...
Gautier, S., Morchadi, R.: A selection of convex-compact-valued multi-functions with remarkable properties: the Steiner selection. Numer. Funct. Anal. Optim. 13 (5–6), 513–522 (1992)A selection of convex-compact-valued multi-functions with remarkable properties: the Steiner selection. ...
Some basic properties of certain subclass of harmonic univalent functionsAnalyticunivalentstarlikeconvex functionsclose-to-convexharmonic functionssubordinationcoefficient estimatesconvolutionPrimary: 30C45We consider the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of ...
Section 1.4 is devoted to continuous plurisubharmonic and strictly plurisubharmonic C 2 -functions. In Section 1.5, by means of these functions, pseudoconvex and strictly pseudoconvex open sets are introduced. We prove that every domain of holomorphy is pseudoconvex, but the converse (Levi's ...