@article{Aydi2024, 
author = {Hassen Aydi and Bessem Samet and Manuel De la Sen},
title = {On    ψ-convex functions and related inequalities},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {11139-11155},
keywords = {ψ-convex functions, Hermite-Hadamard-type inequalities, Simpson-type inequalities},
url = {https://www.sciopen.com/article/10.3934/math.2024546},
doi = {10.3934/math.2024546},
abstract = {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  ∈      C    1    (  [  0  ,  ∞  )  ) such that        |        f    ′        |   is    ψ-convex. Our obtained results are new and recover several existing results from the literature.}
}