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December 2020 Hermite–Hadamard inequality for semiconvex functions of rate $(k_1,k_2)$ on the coordinates and optimal mass transportation
Ping Chen, Wing-Sum Cheung
Rocky Mountain J. Math. 50(6): 2011-2021 (December 2020). DOI: 10.1216/rmj.2020.50.2011

Abstract

We give a new Hermite–Hadamard inequality for a function f:[a,b]×[c,d]2 which is semiconvex of rate (k1,k2) on the coordinates. This generalizes some existing results on Hermite–Hadamard inequalities of S. S. Dragomir. In addition, we explain the Hermite–Hadamard inequality from the point of view of optimal mass transportation with cost function c(x,y):=f(yx)+k12|x1y1|2+k22|x2y2|2, where f():[a,b]×[c,d][0,) is semiconvex of rate (k1,k2) on the coordinates and x=(x1,x2), y=(y1,y2)[a,b]×[c,d].

Citation

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Ping Chen. Wing-Sum Cheung. "Hermite–Hadamard inequality for semiconvex functions of rate $(k_1,k_2)$ on the coordinates and optimal mass transportation." Rocky Mountain J. Math. 50 (6) 2011 - 2021, December 2020. https://doi.org/10.1216/rmj.2020.50.2011

Information

Received: 26 November 2019; Accepted: 10 February 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.2011

Subjects:
Primary: 26B25, 26D15, 49Q20

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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