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arXiv · 1710.07182

Positivity of sums and integrals for higher order nabla-convex and completely monotonic functions

Faraz Mehmood·Asif R. Khan·Muhammad Adnan
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Abstract

We extend the definitions of $\nabla-$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type for sum $\sum \sum p_{ij} f(y_i, z_j)$ and integrals $\int P(y)f(y) dy$, $\int \int P(y,z) f(y,z) dy \, dz$ 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.

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Faraz Mehmood, Asif R. Khan, Muhammad Adnan. 2017-10-13. Positivity of sums and integrals for higher order nabla-convex and completely monotonic functions. https://arxiv.org/abs/1710.07182

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