In this note, we give a counterexample to show that Hadamard's inequality does not hold on a polyhedron in multi-dimensional Euclidean space. Then we give a sufficient condition on the polyhedron for Hadamard's inequality to hold. Finally, we provide an approach to create a large class of polyhedra
Two new mappings associated with Hadamard's inequalities for convex functions
β Scribed by S.S. Dragomir; R.P. Agarwal
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 279 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we shall introduce two new mappings closely connected with Hadamard's inequality for convex mappings and study their main properties. Some applications are also included.
π SIMILAR VOLUMES
In this paper, some inequalities of Hadamard's type for quasi-convex functions are given. Some error estimates for the Trapezoidal formula are obtained. Applications to some special means are considered.
New fixed-point theorems for two maps defined on product spaces are obtained. These new results only require one of them to satisfy a noncompactness condition. Previous results required each map to satisfy a noncompactness condition. Applications of our results are given to intersection problems for
This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solutio