FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4308919616> ?p ?o ?g. }

• W4308919616 endingPage "261" @default.
• W4308919616 startingPage "241" @default.
• W4308919616 abstract "Given a set H of functions defined on a set X, á function f:X↦R¯ is called abstract H-convex if it is the upper envelope of its H-minorants, i.e. such its minorants which belong to the set H; and f is called regularly abstract H-convex if it is the upper envelope of its maximal (with respect to the pointwise ordering) H-minorants. In the paper we first present the basic notions of (regular) H-convexity for the case when H is an abstract set of functions. For this abstract case a general sufficient condition based on Zorn's lemma for a H-convex function to be regularly H-convex is formulated. The goal of the paper is to study the particular class of regularly H-convex functions, when H is the set LCˆ(X,R) of real-valued Lipschitz continuous classically concave functions defined on a real normed space X. For an extended-real-valued function f:X↦R¯ to be LCˆ-convex it is necessary and sufficient that f be lower semicontinuous and bounded from below by a Lipschitz continuous function; moreover, each LCˆ-convex function is regularly LCˆ-convex as well. We focus on LCˆ-subdifferentiability of functions at a given point. We prove that the set of points at which an LCˆ-convex function is LCˆ-subdifferentiable is dense in its effective domain. This result extends the well-known classical Brøndsted-Rockafellar theorem on the existence of the subdifferential for convex lower semicontinuous functions to the more wide class of lower semicontinuous functions. Using the subset LCˆθ of the set LCˆ consisting of such Lipschitz continuous concave functions that vanish at the origin we introduce the notions of LCˆθ-subgradient and LCˆθ-subdifferential of a function at a point which generalize the corresponding notions of the classical convex analysis. Some properties and simple calculus rules for LCˆθ-subdifferentials as well as LCˆθ-subdifferential conditions for global extremum points are established. Symmetric notions of abstract LCˇ-concavity and LCˇ-superdifferentiability of functions where LCˇ:=LCˇ(X,R) is the set of Lipschitz continuous convex functions are also considered." @default.
• W4308919616 created "2022-11-19" @default.
• W4308919616 creator A5056059552 @default.
• W4308919616 date "2022-11-11" @default.
• W4308919616 modified "2023-09-27" @default.
• W4308919616 title "Regularly abstract convex functions with respect to the set of Lipschitz continuous concave functions" @default.
• W4308919616 cites W1026993568 @default.
• W4308919616 cites W1523004878 @default.
• W4308919616 cites W2027013172 @default.
• W4308919616 cites W2041103116 @default.
• W4308919616 cites W2043688950 @default.
• W4308919616 cites W2049138554 @default.
• W4308919616 cites W2058630058 @default.
• W4308919616 cites W2067243588 @default.
• W4308919616 cites W2078762555 @default.
• W4308919616 cites W2089447917 @default.
• W4308919616 cites W2090268690 @default.
• W4308919616 cites W2766276860 @default.
• W4308919616 cites W2891032710 @default.
• W4308919616 cites W2913806414 @default.
• W4308919616 cites W3022146564 @default.
• W4308919616 cites W3080797833 @default.
• W4308919616 cites W3156884384 @default.
• W4308919616 cites W3158532942 @default.
• W4308919616 cites W4240506259 @default.
• W4308919616 cites W4249513058 @default.
• W4308919616 cites W4303084602 @default.
• W4308919616 cites W58439901 @default.
• W4308919616 cites W591794949 @default.
• W4308919616 doi "https://doi.org/10.1080/02331934.2022.2145173" @default.
• W4308919616 hasPublicationYear "2022" @default.
• W4308919616 type Work @default.
• W4308919616 citedByCount "0" @default.
• W4308919616 crossrefType "journal-article" @default.
• W4308919616 hasAuthorship W4308919616A5056059552 @default.
• W4308919616 hasBestOaLocation W43089196162 @default.
• W4308919616 hasConcept C106159729 @default.
• W4308919616 hasConcept C112680207 @default.
• W4308919616 hasConcept C114614502 @default.
• W4308919616 hasConcept C118615104 @default.
• W4308919616 hasConcept C12108790 @default.
• W4308919616 hasConcept C134306372 @default.
• W4308919616 hasConcept C145446738 @default.
• W4308919616 hasConcept C157972887 @default.
• W4308919616 hasConcept C162324750 @default.
• W4308919616 hasConcept C200661725 @default.
• W4308919616 hasConcept C202444582 @default.
• W4308919616 hasConcept C206194317 @default.
• W4308919616 hasConcept C22324862 @default.
• W4308919616 hasConcept C2524010 @default.
• W4308919616 hasConcept C2777984123 @default.
• W4308919616 hasConcept C33923547 @default.
• W4308919616 hasConcept C34388435 @default.
• W4308919616 hasConcept C49870271 @default.
• W4308919616 hasConcept C58385900 @default.
• W4308919616 hasConcept C6018138 @default.
• W4308919616 hasConcept C66690126 @default.
• W4308919616 hasConcept C72134830 @default.
• W4308919616 hasConceptScore W4308919616C106159729 @default.
• W4308919616 hasConceptScore W4308919616C112680207 @default.
• W4308919616 hasConceptScore W4308919616C114614502 @default.
• W4308919616 hasConceptScore W4308919616C118615104 @default.
• W4308919616 hasConceptScore W4308919616C12108790 @default.
• W4308919616 hasConceptScore W4308919616C134306372 @default.
• W4308919616 hasConceptScore W4308919616C145446738 @default.
• W4308919616 hasConceptScore W4308919616C157972887 @default.
• W4308919616 hasConceptScore W4308919616C162324750 @default.
• W4308919616 hasConceptScore W4308919616C200661725 @default.
• W4308919616 hasConceptScore W4308919616C202444582 @default.
• W4308919616 hasConceptScore W4308919616C206194317 @default.
• W4308919616 hasConceptScore W4308919616C22324862 @default.
• W4308919616 hasConceptScore W4308919616C2524010 @default.
• W4308919616 hasConceptScore W4308919616C2777984123 @default.
• W4308919616 hasConceptScore W4308919616C33923547 @default.
• W4308919616 hasConceptScore W4308919616C34388435 @default.
• W4308919616 hasConceptScore W4308919616C49870271 @default.
• W4308919616 hasConceptScore W4308919616C58385900 @default.
• W4308919616 hasConceptScore W4308919616C6018138 @default.
• W4308919616 hasConceptScore W4308919616C66690126 @default.
• W4308919616 hasConceptScore W4308919616C72134830 @default.
• W4308919616 hasIssue "1" @default.
• W4308919616 hasLocation W43089196161 @default.
• W4308919616 hasLocation W43089196162 @default.
• W4308919616 hasOpenAccess W4308919616 @default.
• W4308919616 hasPrimaryLocation W43089196161 @default.
• W4308919616 hasRelatedWork W165488893 @default.
• W4308919616 hasRelatedWork W2005700899 @default.
• W4308919616 hasRelatedWork W2385354747 @default.
• W4308919616 hasRelatedWork W2977850992 @default.
• W4308919616 hasRelatedWork W3022146564 @default.
• W4308919616 hasRelatedWork W3176738824 @default.
• W4308919616 hasRelatedWork W4225613552 @default.
• W4308919616 hasRelatedWork W4300188432 @default.
• W4308919616 hasRelatedWork W4320176170 @default.
• W4308919616 hasRelatedWork W4361981423 @default.
• W4308919616 hasVolume "72" @default.
• W4308919616 isParatext "false" @default.
• W4308919616 isRetracted "false" @default.

• next