A Mean Value Theorem for Tangentially Convex Functions

Juan Enrique Martinez Legaz

doi:https://doi.org/10.1007/s11228-023-00674-3

A Mean Value Theorem for Tangentially Convex Functions

Juan Enrique Martinez Legaz

Department of Economics and Economic History

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Abstract

The main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions. The new mean value theorem is then applied, analogously to what is done in the classical case, to characterize, in the tangentially convex context, Lipschitz functions, increasingness with respect to the ordering induced by a closed convex cone, convexity, and quasiconvexity.

Translated title of the contribution	Un teorema del valor medio para funciones tangencialmente convexas
Original language	English
Article number	13
Number of pages	10
Journal	Set-Valued Analysis
Volume	31
Issue number	2
DOIs	https://doi.org/10.1007/s11228-023-00674-3
Publication status	Published - 27 Mar 2023

Keywords

Convexity
Mean value theorem
Monotonicity
Quasiconvexity
Quasimonotonicity
Tangential convexity
Tangential subdifferential

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author = "{Martinez Legaz}, {Juan Enrique}",

note = "I gratefully acknowledge financial support from the Spanish Ministry of Science, Innovation and Universities, through the grant PGC2018-097960-B-C21 and the Severo Ochoa Program for Centers of Excellence in R&D (CEX2019-000915-S). I am affiliated with MOVE (Markets, Organizations and Votes in Economics).",

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N2 - The main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions. The new mean value theorem is then applied, analogously to what is done in the classical case, to characterize, in the tangentially convex context, Lipschitz functions, increasingness with respect to the ordering induced by a closed convex cone, convexity, and quasiconvexity.

AB - The main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one for differentiable functions, as well as Wegge theorem for convex functions. The new mean value theorem is then applied, analogously to what is done in the classical case, to characterize, in the tangentially convex context, Lipschitz functions, increasingness with respect to the ordering induced by a closed convex cone, convexity, and quasiconvexity.

KW - Teorema del valor medio, convexidad tangencia, subdiferencial tangencial, convexidad, monotonía, cuasiconvexida, cuasimonotonía

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KW - Mean value theorem

KW - Monotonicity

KW - Quasiconvexity

KW - Quasimonotonicity

KW - Tangential convexity

KW - Tangential subdifferential

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A Mean Value Theorem for Tangentially Convex Functions

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Keywords

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