@article{Aydi2024, 
author = {Hassen Aydi and Bessem Samet and Manuel De la Sen},
title = {A generalization of convexity via an implicit inequality},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {11992-12010},
keywords = {convexity, implicit inequality, (ζ, w)-admissible functions, integral inequalities, Hermite-Hadamard-type inequalities},
url = {https://www.sciopen.com/article/10.3934/math.2024586},
doi = {10.3934/math.2024586},
abstract = {We unified several kinds of convexity by introducing the class              A              ζ      ,      w        (  [  0  ,  1  ]  ×      I    2    ) 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  ]  ×      I    2    ) for some    ζ  ∈  C  (  [  0  ,  1  ]  ) and    w  ∈      C    1    (  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.}
}