On ψ-convex functions and related inequalities

Hassen Aydi*, Bessem Samet, Manuel De la Sen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce the class of ψ-convex functions f: [0, ∞) → ℝ, where ψ ∈ C([0, 1]) satisfies ψ ≥ 0 and ψ(0) ≠ ψ(1). This class includes several types of convex functions introduced in previous works. We first study some properties of such functions. Next, we establish a double Hermite-Hadamard-type inequality involving ψ-convex functions and a Simpson-type inequality for functions f ∈ C1([0, ∞)) such that | f | is ψ-convex. Our obtained results are new and recover several existing results from the literature.

Original languageEnglish
Pages (from-to)11139-11155
Number of pages17
JournalAIMS Mathematics
Issue number5
Publication statusPublished - 2024
Externally publishedYes


  • Hermite-Hadamard-type inequalities
  • Simpson-type inequalities
  • ψ-convex functions


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