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 journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)11992-12010
Number of pages19
JournalAIMS Mathematics
Issue number5
Publication statusPublished - 2024
Externally publishedYes


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


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