6 papers
Ky Fan inequalities for bivariate means
Alfred Witkowski
In this note we give sufficient conditions for bivariate, homogeneous, symmetric means and to satisfy Ky Fan inequalities $$\frac{M}{M'}<\frac{N}{N'}\qquad\text{ and }\quad…
Another refinement of the right-hand side of the Hermite-Hadamard inequality for simplices
Monika Nowicka, Alfred Witkowski
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.
Inequalities of Levin-Stečkin, Clausing and Chebyshev revisited
Alfred Witkowski
We prove the Levin-Stečkin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof…
Applications of the Hermite-Hadamard inequality
Monika Nowicka, Alfred Witkowski
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 ki…
A refinement of the left-hand side of Hermite-Hadamard inequality for simplices
Monika Nowicka, Alfred Witkowski
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.
Refinement of the right-hand side of Hermite-Hadamard inequality for simplices
Monika Nowicka, Alfred Witkowski
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…