%0 Journal Article
%T Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Mehmood, Faraz
%A Khan, Asif Raza
%A Adnan, Muhammad
%D 2022
%\ 02/01/2022
%V 19
%N 1
%P 119-137
%! Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions
%K Convex functions
%K $nabla-$convex functions
%K completely monotonic functions
%R 10.22130/scma.2021.527460.926
%X 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.
%U https://scma.maragheh.ac.ir/article_249585_172a7aeb2e4fe6ea55ee687557aa2805.pdf