Some generalizations of the convexity
WebFeb 14, 2024 · The Hermite–Hadamard inequality was first considered for convex functions and has been studied extensively. Recently, many extensions were given with the use of … WebDefinition [ edit] The light gray area is the absolutely convex hull of the cross. A subset of a real or complex vector space is called a disk and is said to be disked, absolutely convex, and convex balanced if any of the following equivalent conditions is satisfied: S {\displaystyle S} is a convex and balanced set. for any scalar.
Some generalizations of the convexity
Did you know?
WebFollowing [2] and [4], we x a convex body Pˆ(R+)d; i.e., a compact, convex set in (R+)dwith non-empty interior Po. The most important example is the case where P is the convex hull of a nite subset of (Z +) din (R ) with Po 6= ;(P is a non-degenerate convex polytope). Another interesting class consists of the Webconvex increasing cost function C(d) and a concave in-creasing benefit function B(d). If caught, the villager’s benefit is 0 (the extracted resources are confiscated) but the cost is unchanged (the extractor’s traveled distance does not change; there is no positive punishment beyond the confiscation itself and being prevented from engag-
WebThere are many types of convexity in the literature. The three types of convexity that will be used in this article are as follows. The concept of s-convex function was introduced in … WebAbstract. In this paper, we present some generalizations of an inequality of Hardy-Littlewood-Polya. We give the n-exponential convexity and log-convexity of the functions …
http://www.hjms.hacettepe.edu.tr/uploads/717d9103-00cc-403c-87c8-8c10edf6f60f.pdf WebSome landmarks in this line of research are the fractional Helly theorm of Kalai and the (p, q)-theorem of Alon and Kleitman. See for instance the textbooks [Mat02, Bár21] or the …
WebNov 12, 2024 · 4 Conclusion. We find an example for η -convex function defined on rectangle is not convex. The authors define a coordinate (\eta _ {1}, \eta _ {2}) -convex function and …
WebMay 1, 2012 · In this article, the concept of convexity is considered. Generalizations of this concept, that were examined by different authors, are briefly given. In this paper, a study … incarnation\\u0027s acWebMar 8, 2012 · Generalizations of this concept, that were examined by different authors, are briefly given. In this paper, a study of two forms of abstract convexity is undertaken: one … incarnation\\u0027s afWebThe main findings were effectively composed of convex functions and their properties. The results. This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. incarnation\\u0027s aeWebJoosten [5] introduced the family of “α-egalitarian” Shapley values as the convex combinations φα = αSh +(1 −α)ED for any scalar α between 0 and 1, where ED represents the equal division solution given by EDi(N,v)= v(N) n for all i ∈ N.In van den Brink et al. [6], the authors considered the question of the consistency of inclusions gallery sfWebclass, but he did note that it includes all convex functions and some non-convex functions. FENCHEL [121 was one of the early pioneers in formalizing, naming, and developing the … inclusions galleryincarnation\\u0027s amWebTheorem 15. Let f be a -strongly convex function with respect to some norm kkand let x i be any sequencesuchthat f(x i+1) min y f(y)+ L 2 ky x ik2 thenwehavethat f(x k) f 1 L+ k [f(x 0) … incarnation\\u0027s ag