Convexity theory on spherical spaces (I)

Abstract In this study, we work with the relative divergence of type s,s\in {\mathbb{R}} , which includes the Kullback-Leibler divergence and the Hellinger and χ 2 distances as particular cases. We study the symmetrized divergences in additive and multiplicative forms. Some basic properties such as symmetry, monotonicity and log-convexity are established. An important result from the convexity theory is also proved.

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Vanishing of certain equivariant distributions on spherical spaces for quasi-split groups

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2021.106870 ◽

2021 ◽

pp. 106870

Author(s):

Hengfei Lu

Keyword(s):

Spherical Spaces

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On the Volume of a Symmetric Tetrahedron in Hyperbolic and Spherical Spaces

Siberian Mathematical Journal ◽

10.1023/b:simj.0000042473.53530.56 ◽

2004 ◽

Vol 45 (5) ◽

pp. 840-848 ◽

Cited By ~ 11

Author(s):

D. A. Derevnin ◽

A. D. Mednykh ◽

M. G. Pashkevich

Keyword(s):

Spherical Spaces

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New Integral Inequalities via Generalized Preinvex Functions

Axioms ◽

10.3390/axioms10040296 ◽

2021 ◽

Vol 10 (4) ◽

pp. 296

Author(s):

Muhammad Tariq ◽

Asif Ali Shaikh ◽

Soubhagya Kumar Sahoo ◽

Hijaz Ahmad ◽

Thanin Sitthiwirattham ◽

...

Keyword(s):

Integral Inequality ◽

Type Inequality ◽

Integral Inequalities ◽

Power Mean ◽

Science And Engineering ◽

Special Means ◽

Algebraic Properties ◽

Convexity Theory ◽

Hölder’S Integral Inequality ◽

Preinvex Functions

The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex function and to present inequalities of the Hermite–Hadamard type in the setting of the generalized s-type m–preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite–Hadamard-type inequality using Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory.

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Busemann's intersection inequality in hyperbolic and spherical spaces

Advances in Mathematics ◽

10.1016/j.aim.2018.01.008 ◽

2018 ◽

Vol 326 ◽

pp. 521-560 ◽

Cited By ~ 1

Author(s):

Susanna Dann ◽

Jaegil Kim ◽

Vladyslav Yaskin

Keyword(s):

Spherical Spaces

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On the symmetrized S-divergence

ITM Web of Conferences ◽

10.1051/itmconf/20192901004 ◽

2019 ◽

Vol 29 ◽

pp. 01004

Author(s):

Slavko Simić

Keyword(s):

Leibler Divergence ◽

Convexity Theory ◽

Relative Divergence

In this paper we worked with the relative divergence of type s, s ∈ ℝ, which include Kullback-Leibler divergence and the Hellinger and χ2 distances as particular cases. We give here a study of the sym- metrized divergences in additive and multiplicative forms. Some ba-sic properties as symmetry, monotonicity and log-convexity are estab-lished. An important result from the Convexity Theory is also proved.

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