@article{Samet2026, 
author = {Bessem Samet},
title = {On    k–Airy convexity and applications to eigenvalue problems},
year = {2026},
journal = {Networks and Heterogeneous Media},
volume = {21},
number = {2},
pages = {476-495},
keywords = {Airy functions, k–Airy convex functions, Airy differential equation, eigenvalue problems},
url = {https://www.sciopen.com/article/10.3934/nhm.2026022},
doi = {10.3934/nhm.2026022},
abstract = {Let              A      i       and              B      i       denote the Airy functions. For a fixed    k  >  0, we introduce the class                      A        i        r        y              k    (      I    ) of    k–Airy convex functions on an interval        I    ⊂  [  0  ,  ∞  ). A function    f  :      I    →      R   is called    k–Airy convex on        I   if, for every subinterval    [  a  ,  b  ]  ⊂      I   and all    a  <  t  <  b,      f  (  t  )    ≤                                A          i                    (      k      t      )                              B          i                    (      k      b      )      −                        A          i                    (      k      b      )                              B          i                    (      k      t      )                                A          i                    (      k      a      )                              B          i                    (      k      b      )      −                        A          i                    (      k      b      )                              B          i                    (      k      a      )          f  (  a  )    +                                A          i                    (      k      a      )                              B          i                    (      k      t      )      −                        A          i                    (      k      t      )                              B          i                    (      k      a      )                                A          i                    (      k      a      )                              B          i                    (      k      b      )      −                        A          i                    (      k      b      )                              B          i                    (      k      a      )          f  (  b  )  .We establish fundamental properties of                      A        i        r        y              k    (      I    ). As an application, we derive lower bounds for eigenvalues in Airy-type boundary value problems.}
}