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Harmonically m-Concave Set-Valued Function

Gabriel Santana, Maira Valera-López, Nelson Merentes

Abstract

This research aimed to introduce the concept of harmonically m-concave set-valued functions, which is obtained from the combination of two definitions: harmonically m-concave functions and set-valued functions. In this work some properties and characteristics are developed, as well as a Kuhn type theorem and Bernstein-Doetcsh type result for such functions.

Harmonically m-Concave Set-Valued Function

Abstract

This research aimed to introduce the concept of harmonically m-concave set-valued functions, which is obtained from the combination of two definitions: harmonically m-concave functions and set-valued functions. In this work some properties and characteristics are developed, as well as a Kuhn type theorem and Bernstein-Doetcsh type result for such functions.
Paper Structure (3 sections, 11 theorems, 52 equations)

This paper contains 3 sections, 11 theorems, 52 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Main Results

Key Result

Theorem 2.9

(see santana2020(2)) Let $D$ a harmonically convex subset of $X$ and $t\in (0,1)$ a fixed point. If the set-valued function $F:D\rightarrow cc(Y)$ is strongly harmonically t-concave modulus $c$, then $F$ is strongly harmonically midconcave modulus $c$.

Theorems & Definitions (31)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Remark 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Definition 2.8
  • Theorem 2.9
  • Lemma 2.10
  • ...and 21 more