On $m$-convexity of set-valued functions

Teodoro Lara; Nelson Merentes; Roy Quintero; Edgar Rosales

doi:10.15352/aot.1810-1429

Abstract

‎We introduce the notion of an $m$-convex set-valued function and study some properties of this class of functions‎. ‎Several characterizations are given as well as certain algebraic properties and examples‎. ‎Finally‎, ‎an inclusion of Jensen type is presented jointly with a sandwich type theorem‎.

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Teodoro Lara. Nelson Merentes. Roy Quintero. Edgar Rosales. "On $m$-convexity of set-valued functions." Adv. Oper. Theory 4 (4) 767 - 783, Autumn 2019. https://doi.org/10.15352/aot.1810-1429

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Received: 23 October 2018; Accepted: 4 March 2019; Published: Autumn 2019

First available in Project Euclid: 15 May 2019

zbMATH: 07064104

MathSciNet: MR3949974

Digital Object Identifier: 10.15352/aot.1810-1429

Subjects:

Primary: 26A51‎

Secondary: 47H04 , 52A30

Keywords: $m$-convex set‎ , $m$-convex set-valued function , Jensen type inclusion‎ , ‎sandwich theorem

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