Positivity of Integrals for Higher Order $nabla-$Convex and Completely Monotonic Functions

Author(s):

Faraz Mehmood * , Asif Khan , Muhammad Adnan

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
We extend the definitions of $nabla-$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals $int P(y)f(y) dy$ and $int int P(y,z) f(y,z) dy   dz$ are deduced. Using obtained identities, positivity of these expressions are characterized for  higher order $nabla-$convex and completely monotonic functions. Some applications in terms of generalized Cauchy means and exponential convexity are given.
Keywords:

Convex functions , $nabla-$convex functions , completely monotonic functions

Language:
English
Published:
Sahand Communications in Mathematical Analysis, Volume:19 Issue: 1, Winter 2022
Pages:
119 to 137
https://www.magiran.com/p2407206