Additive ρ-Functional Inequalities and Their Applications

Mathematical Analysis and Applications - Springer Optimization and Its Applications ◽

10.1007/978-3-030-31339-5_14 ◽

2019 ◽

pp. 391-410

Author(s):

Jung Rye Lee ◽

Choonkil Park ◽

Themistocles M. Rassias ◽

Xiaohong Zhang

Keyword(s):

Functional Inequalities

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Bi-additive s-functional inequalities and biderivation in modular spaces

The Journal of Analysis ◽

10.1007/s41478-021-00311-y ◽

2021 ◽

Author(s):

T. L. Shateri

Keyword(s):

Functional Inequalities ◽

Modular Spaces

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Functional Inequalities for Two-Level Concentration

Potential Analysis ◽

10.1007/s11118-021-09900-9 ◽

2021 ◽

Author(s):

Franck Barthe ◽

Michał Strzelecki

Keyword(s):

Sobolev Inequality ◽

Poincaré Inequality ◽

Logarithmic Sobolev Inequality ◽

Probability Measures ◽

Exponential Rate ◽

Functional Inequalities ◽

Concentration Inequality ◽

Poincare Inequality ◽

Free Concentration ◽

Concentration Property

AbstractProbability measures satisfying a Poincaré inequality are known to enjoy a dimension-free concentration inequality with exponential rate. A celebrated result of Bobkov and Ledoux shows that a Poincaré inequality automatically implies a modified logarithmic Sobolev inequality. As a consequence the Poincaré inequality ensures a stronger dimension-free concentration property, known as two-level concentration. We show that a similar phenomenon occurs for the Latała–Oleszkiewicz inequalities, which were devised to uncover dimension-free concentration with rate between exponential and Gaussian. Motivated by the search for counterexamples to related questions, we also develop analytic techniques to study functional inequalities for probability measures on the line with wild potentials.

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On a certain stability of the Hermite–Hadamard inequality

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0291 ◽

2008 ◽

Vol 465 (2102) ◽

pp. 571-583 ◽

Cited By ~ 5

Author(s):

Attila Házy ◽

Zsolt Páles

Keyword(s):

Functional Inequalities ◽

Hadamard Inequality ◽

Real Functions ◽

The Stability

The classical Hermite–Hadamard inequality, under some regularity assumptions, characterizes convexity of real functions. The aim of this paper is to establish connections between the stability forms of the functional inequalities related to Jensen convexity, convexity and the Hermite–Hadamard inequality.

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