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

DOI10.22130/scma.2021.527460.926zbMath1496.26011arXiv1710.07182OpenAlexW4386816548MaRDI QIDQ5097757

Faraz Mehmood, Muhammad Adnan, Asif R. Khan

Publication date: 1 September 2022

Full work available at URL: https://arxiv.org/abs/1710.07182

zbMATH Keywords

convex functionscompletely monotonic functions\(\nabla\)-convex functions

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Functional inequalities, including subadditivity, convexity, etc. (39B62) Convexity of real functions in one variable, generalizations (26A51) Other analytical inequalities (26D20)

Uses Software

• Matlab

Cites Work

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• On some inequalities for \(\nabla\)-convex sequences of higher order
• On some inequalities for convex and \(\nabla\)-convex sequences of higher order. II
• Convex functions, partial orderings, and statistical applications
• A probabilistic interpretation of complete monotonicity
• Exponential convexity, positive semi-definite matrices and fundamental inequalities
• Completely Monotone Functions: A Digest
• A Note on Completely and Absolutely Monotone Functions
• Completely monotonic functions
• Necessary and Sufficient Conditions for the Representation of a Function as a Laplace Integral
• Popoviciu type characterization of positivity of sums and integrals for convex functions of higher order

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