New developments in convexity theory
Constantin P. Niculescu
Center for Nonlinear Anlysis and its Applications,
University of Craiova, Craiova 1100, ROMANIA
The aim of our talk is to report on new results concerning:
- the extension of Choquet theory to signed measures
- the nonlinear theory of integration associated to means
- Jensen inequality for arbitrary positive measures (the results of
Paolo Roselli and Michel Willem)
- 1
- S. S. Dragomir, On Hadamard's inequality for the convex
mappings defined on a ball in the space and applications, Math. Inequal. &
Appl., 3 (2000), 177-187.
- 2
- A. M. Fink, A best possible Hadamard inequality, Math. Inequal. &
Appl., 1 (1998), 223-230.
- 3
- Fuchs L., A new proof of an inequality of Hardy,
Littlewood and Polya, Mat. Tidsskr. B., 1947, pp. 53-54.
- 4
- D. S. Mitrinovic, J. E. Pecaric and A. M. Fink,
Classical and new Inequalities in Analysis, Kluwer Academic Publ.,
Dordrecht, 1993.
- 5
- C. P. Niculescu, Convexity according to the geometric mean, Math.
Inequal. Appl., 3 (2000), 155-167.
-
- 6
- C. P. Niculescu, A Note on the Dual Hermite-Hadamard
Inequality, The Math. Gazette, July 2001.
- 7
- C. P. Niculescu, A multiplicative mean value and its
applications. In vol. Theory of Inequalities and Applications, Nova Science Pubblishers (USA), 2001, edited by
Y.J. Cho, S.S. Dragomir
and J. Kim.
- 8
- C. P. Niculescu, An extension of Chebyshev's Inequality
and its Connection with Jensen's Inequality, J. of Inequal. & Appl.
6 (2001), 451-462.
- 9
- C. P. Niculescu, The Hermite-Hadamard inequality for
functions of a vector variable. Preprint
- 10
- C. P. Niculescu, Convexity according to means. Preprint
- 11
- R. R. Phelps, Lectures on Choquet's Theorem, D. van
Nostrand Company Inc., Princeton, 1966.
- 12
- P. Roselli and M. Willem, A convexity inequality, Amer.
Math. Monthly, to appear.