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Half-discrete Hilbert-type inequalities /
In 1934, G.H. Hardy et al. published a book entitled "Inequalities", in which a few theorems about Hilbert-type inequalities with homogeneous kernels of degree-one were considered. Since then, the theory of Hilbert-type discrete and integral inequalities is almost built by Prof. Bicheng Ya...
| Call Number: | Libro Electrónico |
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| Format: | Electronic eBook |
| Language: | Inglés |
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Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2014.
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| Online Access: | Texto completo |
Table of Contents:
- 1. Recent developments of Hilbert-Type inequalities with applications. 1.1. Introduction. 1.2. Hilbert's inequality and Hilbert's operator. 1.3. Modern research for Hilbert-type inequalities. 1.4. Some new applications for Hilbert-type inequalities. 1.5. Concluding remarks
- 2. Improvements of the Euler-Maclaurin summation formula and applications. 2.1. Introduction. 2.2. Some special functions relating Euler-Maclaurin's summation formula. 2.3. Estimations of the residue term about a class series. 2.4. Two classes of series estimations
- 3. A half-discrete Hilbert-type inequality with a general homogeneous kernel. 3.1. Introduction. 3.2. Some preliminary lemmas. 3.3. Some theorems and corollaries
- 4. A half-discrete Hilbert-type inequality with a non-homogeneous kernel. 4.1. Introduction. 4.2. Some preliminary lemmas. 4.3. Some theorems and corollaries. 4.4. Some particular examples
- 5. Multi-dimensional half-discrete Hilbert-type inequalities. 5.1. Introduction. 5.2. Some preliminary results and lemmas. 5.3. Some inequalities related to a general homogeneous kernel. 5.4. Some inequalities relating a general non-homogeneous kernel
- 6. Multiple half-discrete Hilbert-type inequalities. 6.1. Introduction. 6.2. First kind of multiple Hilbert-type inequalities. 6.3. Second kind of multiple Hilbert-type inequalities. 6.4. Some examples with the particular kernels.