Advances in Operator Theory

On $m$-convexity of set-valued functions

Teodoro Lara, Nelson Merentes, Roy Quintero, and Edgar Rosales

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‎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.

Article information

Adv. Oper. Theory, Volume 4, Number 4 (2019), 767-783.

Received: 23 October 2018
Accepted: 4 March 2019
First available in Project Euclid: 15 May 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A51: Convexity, generalizations
Secondary: 47H04‎ ‎52A30

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


Lara, Teodoro; Merentes, Nelson; Quintero, Roy; Rosales, Edgar. On $m$-convexity of set-valued functions. Adv. Oper. Theory 4 (2019), no. 4, 767--783. doi:10.15352/aot.1810-1429.

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  • S. S. Dragomir, On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math. 33 (2002), no. 1, 55–65.
  • A. Geletu, Introduction to topological spaces and set-valued maps (Lecture notes), Institute of Mathematics. Department of Operations Research & Stochastics Ilmenau University of Technology. August 25, 2006.
  • T. Lara, N. Merentes, Z. Páles, R. Quintero, and E. Rosales, On $m$-convexity on real linear spaces, UPI J. Math. Biostat. 1 (2018), no. 2, 1–16.
  • J. Matkowski and K. Nikodem, Convex set-valued functions on $(0,+\infty)$ and their conjugate, Rocznik Nauk.-Dydakt. Prace Mat. No. 15 (1998), 103–107.
  • K. Nikodem, On concave and midpoint concave set-valued functions, Glasnik Mat. Ser. III 22(42) (1987), no. 1, 69–76.
  • J. Rooin, A. Alikhani and M. Moslehian, Operator $m$-convex functions, Georgian Math. J. 2018, 25(1), 93–107.
  • E. Sadowska, A sandwich with convexity for set-valued functions, Math. Pannon. 7 (1996), no. 1, 163–169.
  • G. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim. Cluj-Napoca (Romania) (1984), 329–338.
  • G. Toader, On a generalization of the convexity, Mathematica (Cluj) 30(53) (1988), no. 1, 83–87.