Some generalizations of the convexity
Webfunctions that are 'almost1 convex has led to many generalizations of the notion of convex functions. Here we survey some of these extensions of convexity and indicate briefly the role they play in optimization theory. Most of the results in Sections 2 to 5 can be found in … WebApr 22, 2024 · In this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity …
Some generalizations of the convexity
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WebThe concept of convexity related to a function has been generalized in several ways. Some of the most important ones are summarized in the next de nition. De nition 3.2 Let Xand Ybe real topological linear spaces, K X, A Y be a convex cone, and f: X!Ybe a mapping. (i) fis said to be A-convexlike on K, if, for any x 1, x 2 2Kand any 2]0;1 ... Web(ii) for each y ∈ X the set {x ∈ X : (x,y) ∈/ X} is convex (or empty). Then X ×{y0} ⊂ M for some y0 ∈ X. Subsequently, Browder [4] obtained in 1968 the following fixed point theorem: Theorem 1. Let X be a nonempty compact convex subset of a Hausdorff topolog-ical vector space and T : X ⊸ X be a map with nonempty convex values and ...
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 WebSOME GENERALIZATIONS OF HELLY'S THEOREM ON CONVEX SETS ALFRED HORN Helly's well known theorem on convex sets states that if F is a family of closed bounded convex …
WebApr 1, 1991 · CONVEXITY STRUCTURES ON TOPOLOGICAL SPACES We introduce in this section the various geometric structures which will generalize ... ALEXANDROV, … http://files.ele-math.com/abstracts/oam-17-16-abs.pdf
WebIn complex geometry and analysis, the notion of convexity and its generalizations play an important role in understanding function behavior. Examples of classes of functions with …
WebTheorem 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) … cineworld beach boulevardWebMay 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 … cineworld basildon \\u0026 imaxWebFeb 8, 2016 · Abstract. The main objective of this article is to introduce a new class of real valued functions that include the well-known class of {m} -convex functions introduced by … dia departures and arrivalsWebaspects of normal ordering in the Weyl algebra and some of its close relatives. ... It includes chapters on convexity and related concepts; inequalities for mean values, sums, functions, operators, ... (s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). cineworld beachWebIn many cases, in spite of the nonconvexity of these functions, they retain some of the nice properties and characteristics of convex functions. This led to generalizations of the … cineworld bd1 5ldWebGeneralizations of converse Jensen´s inequality and related… diades of pellaWebOct 24, 2011 · E-convexity as a generalization of convexity has been introduced and studied in some recent publications in the fields of pure and applied mathematical analysis.In this … diadem warriors edge pickleball paddle