| 1. |
|
|
| 2. |
|
|
| 3. |
- Barza, Sorina, et al.
(author)
-
Sharp multidimensional multiplicative inequalities for weighted Lp spaces with homogeneous weights
- 1998
-
In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 1:1, s. 53-67
-
Journal article (peer-reviewed)abstract
- Let Ω be an arbitrary cone in IRn with the origin as a vertex. A multidimensional multiplicative inequality for weighted Lp(Ω) -spaces with homogeneous weights is proved. The inequality is sharp and all cases of equality are pointed out. In particular, this inequality may be regarded as a weighted multidimensional extension of previous inequalities of Carlson, Beurling and Leviri.
|
|
| 4. |
- Isac, George, et al.
(author)
-
Inequalities related to isotonicity of projection and antiprojection operators
- 1998
-
In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 1:1, s. 85-97
-
Journal article (peer-reviewed)abstract
- The metric projection operator is an important tool in numerical analysis, optimization, variational inequalities and complementarity problems and has been considered from the point of view of isotonicity, with respect to an ordering compatible with the vector structure on Hilbert spaces and Banach spaces. In this paper, the authors study some inequalities related to the isotonicity of the metric projection operator onto a closed convex set in an ordered Banach space. The concept of antiprojection operator onto a compact nonempty subset of a Hilbert space is introduced and the relationship between the new inequality obtained by the authors and the isotonicity of such an operator is also discussed.
|
|
| 5. |
- Maligranda, Lech
(author)
-
Why Hölder's inequality should be called Rogers' inequality
- 1998
-
In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 1:1, s. 69-83
-
Journal article (peer-reviewed)abstract
- This reviewer remembers Leopold Fejér (1880-1959) saying (in Hungarian) that ``the history of mathematics serves to prove that nobody discovered anything: there was always somebody who had known it before'' (quoted in English in the present paper). The author argues convincingly about who had priority to the inequalities of Hölder (Rogers), Cauchy (Lagrange), Jensen (Hölder) and others. Also equivalences and relations between different forms and different inequalities and several proofs are offered. The paper concludes with biographical sketches of Leonard James Rogers and Otto Ludwig Hölder.
|
|
| 6. |
- Persson, Lars-Erik, et al.
(author)
-
Some difference inequalities with weights and interpolation
- 1998
-
In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 1:3, s. 437-444
-
Journal article (peer-reviewed)abstract
- The well-known Grisvard-Jakovlev inequality (see Theorems 1 and 1_ ) can be interpretedas a fractional order Hardy inequality or as a weighted difference inequality. Someinequalities of this type have been recently proved and discussed by the authors and H. Heinig,and this paper coincides mostly with a lecture held by the first author at the International workshopon difference and differential inequalities (July 3 - 7, 1996, Marmara Research Center,Turkey) where some historical remarks, ideas and results from the papers of the authors and H.Heinig have been presented. Additionally we present and prove some new difference inequalitieswith weights. Mostly, we omit the proofs which can be found in the papers mentioned and in thereferences there, and for simplicity, we consider functions on the interval
|
|
