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

Journal: Sahand Communications in Mathematical Analysis (Vol.19, No. 1)

Publication Date:

Authors : ; ; ;

Page : 119-137

Keywords : Convex functions; $nabla-$convex functions; completely monotonic functions;

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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.

Last modified: 2022-07-31 17:26:09