A generalization of convexity via an implicit inequality

Hassen Aydi; Bessem Samet; Manuel De la Sen

doi:10.3934/math.2024586

A generalization of convexity via an implicit inequality

Hassen Aydi^*, Bessem Samet, Manuel De la Sen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We unified several kinds of convexity by introducing the class A_ζ,w ([0, 1] × I²) of (ζ, w)-admissible functions F: [0, 1] × I × I → R. Namely, we proved that most types of convexity from the literature generate functions F ∈ A_ζ,w ([0, 1] × I²) for some ζ ∈ C([0, 1]) and w ∈ C¹ (I) with w(I) ⊂ I and w^′ > 0. We also studied some properties of (ζ, w)-admissible functions and established some integral inequalities that unify various Hermite-Hadamard-type inequalities from the literature.

Original language	English
Pages (from-to)	11992-12010
Number of pages	19
Journal	AIMS Mathematics
Volume	9
Issue number	5
DOIs	https://doi.org/10.3934/math.2024586
Publication status	Published - 2024
Externally published	Yes

Keywords

(ζ, w)-admissible functions
Hermite-Hadamard-type inequalities
convexity
implicit inequality
integral inequalities

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10.3934/math.2024586

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keywords = "(ζ, w)-admissible functions, Hermite-Hadamard-type inequalities, convexity, implicit inequality, integral inequalities",

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AU - Samet, Bessem

AU - De la Sen, Manuel

PY - 2024

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AB - We unified several kinds of convexity by introducing the class Aζ,w ([0, 1] × I2) of (ζ, w)-admissible functions F: [0, 1] × I × I → R. Namely, we proved that most types of convexity from the literature generate functions F ∈ Aζ,w ([0, 1] × I2) for some ζ ∈ C([0, 1]) and w ∈ C1 (I) with w(I) ⊂ I and w′ > 0. We also studied some properties of (ζ, w)-admissible functions and established some integral inequalities that unify various Hermite-Hadamard-type inequalities from the literature.

KW - (ζ, w)-admissible functions

KW - Hermite-Hadamard-type inequalities

KW - convexity

KW - implicit inequality

KW - integral inequalities

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DO - 10.3934/math.2024586

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VL - 9

SP - 11992

EP - 12010

JO - AIMS Mathematics

JF - AIMS Mathematics

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ER -

A generalization of convexity via an implicit inequality

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