Name Title and Abstract Jean-Christophe Bourin
Matrix Versions of some Classical Inequalities
Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type inequalities. The matrix approach may also provide simplified proofs and new results for classical inequalities. This talk is intended to a large audience, and some open questions will be raised.
Bounds for Zeta and Related Functions
Sharp bounds are obtained for expressions involving Zeta and related functions at a distance of one apart. Since Euler discovered in 1736 a closed form expression for the Zeta function at the even integers, a comparable expression for the odd integers has not been forthcoming. The current article derives sharp bounds for the Zeta, Lambda and Eta functions at a distance of one apart. The methods developed allow an accurate approximation of the function values at the odd integers in terms of the neighbouring known function at even integer values. The Dirichlet Beta function which has explicit representation at the odd integer values is also investigated in the current. Work. Chebyshev functional bounds are utilised to obtain tight upper bounds for the Zeta function at the odd integers.
Sever S. Dragomir
A Survey on Reverses of Schwarz and Triangle Inequality in Inner Product Spaces
The purpose of this talk is to survey recent results concerning reverses of the Schwarz inequality in real or complex inner product spaces that generalise the classical inequalities due to Pólya-Szegö (1925), Cassels (1955), Greub-Reinboldt (1959), Shisha-Mond (1967), and Klamkin-McLenaghan (1977). These results are then employed to provide various reverses for the triangle inequality that will complement the famous result of Diaz-Metcalf (1966) in inner product spaces. The latest inequality is in its turn a generalisation for the classical reverses of the triangle inequality for complex numbers obtained by Petrovich (1917), Marden (1949) and Wilf (1963), which have been extensively used by the last two authors in locating the roots of complex polynomials.
Alexander M. Rubinov
Abstract Convexity and Hermite-Hadamard-type Inequalities
We discuss some applications of abstract convexity for examination of Hermitte-Hadamard-type inequalities. In particular these inequalities for increasing convex-along-rays functions are given. Examples for some domains including triangles and squares are also presented.
This talk is based on a paper by S. Dragomir, A. Rubinov and J. Dutta
In this talk I will give a brief account of some integral inequalities for single, double and triple integrals.
Dynamic Equations on Time Scales
"Dynamic equations on time scales" is a new and quite general concept which aims to extend the theory and applications of continuous and discrete dynamical systems. The time-scale theory has the potential to accurately describe phenomena where continuous and discrete aspects may both appear in the one model.
I will outline the 'time-scale calculus' and then talk about their associated dynamic equations, which generalise the concept of differential and difference equations.
This talk is designed for a wide audience and will be at an introductory level.
To be confirmed
Title of Talk
George Hanna Jerry J. Koliha Nyamwala Fredrick Oluoch Jamal Rooin
On Ky Fan's Inequality
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