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pro vyhledávání: '"Witkowski, Alfred"'
Autor:
Witkowski, Alfred
In this note we give sufficient conditions for bivariate, homogeneous, symmetric means $M$ and $N$ to satisfy Ky Fan inequalities $$\frac{M}{M'}<\frac{N}{N'}\qquad\text{ and }\quad \frac{1}{M}-\frac{1}{M'}<\frac{1}{N}-\frac{1}{N'}.$$
Externí odkaz:
http://arxiv.org/abs/1901.00337
Autor:
Nowicka, Monika, Witkowski, Alfred
Publikováno v:
Aequat. Math. (2018) 92: 1163
In this paper, we establish a new refinement of the right-hand side of Hermite-Hadamard inequality for convex functions of several variables defined on simplices.
Externí odkaz:
http://arxiv.org/abs/1801.01297
Autor:
Witkowski, Alfred
We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality .
Externí odkaz:
http://arxiv.org/abs/1612.05373
Autor:
Witkowski, Alfred
Publikováno v:
The American Mathematical Monthly, 2020 Feb 01. 127(2), 139-139.
Externí odkaz:
https://www.jstor.org/stable/48661473
Autor:
Nowicka, Monika, Witkowski, Alfred
Publikováno v:
Math. Inequal. Appl., (19) 4 (2016), 1319-1334
We show how the recent improvement of the Hermite-Hadamard inequality can be applied to some (not necessarily convex) planar figures and three-dimensional bodies satisfying some kind of regularity.
Externí odkaz:
http://arxiv.org/abs/1603.07170
Autor:
Nowicka, Monika, Witkowski, Alfred
Publikováno v:
J. Inequal. Appl. (2015) 2015:373
In this paper, we establish a new refinement of the left-hand side of Hermite-Hadamard inequality for convex functions of several variables defined on simplices.
Externí odkaz:
http://arxiv.org/abs/1509.03260
Autor:
Nowicka, Monika, Witkowski, Alfred
Publikováno v:
Aequat. Math., 91 (2017), 121-128
We establish a new refinement of the right-hand side of the Hermite-Hadamard inequality for simplices, based on the average values of a convex function over the faces of a simplex and over the values at their barycenters.
Comment: Correctet stat
Comment: Correctet stat
Externí odkaz:
http://arxiv.org/abs/1509.02569
Publikováno v:
Results Math., 71(1) (2017), 397-410
Extending the notion of projective means we first generalize an invariance identity related to the Carlson log given in a recent paper of P. Kahlig and J. Matkowski, and then, more generally, given a bivariate symmetric, homogeneous and monotone mean
Externí odkaz:
http://arxiv.org/abs/1501.02356
Akademický článek
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Autor:
MATKOWSKI, JANUSZ, WITKOWSKI, ALFRED
Publikováno v:
The Mathematical Gazette, 2018 Nov 01. 102(555), 517-520.
Externí odkaz:
https://www.jstor.org/stable/26539049