Discrete Multiple Hilbert Type Inequality With Non-Homogeneous Kernel

Ban, Biserka Draščić; Pečarić, Josip; Perić, I.; Pogány, Tibor K.

doi:10.4134/jkms.2010.47.3.537

Cited by 3 publications

(1 citation statement)

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“…Therefore, this article gives, for the first time, a complete overview of the author's method for obtaining a whole class of Hilbert's inequalities for the bilinear form (2) generated either by the non-homogeneous and/or homogeneous kernel function K. The exhaustive reference list covers all publication items in which the interested reader can clearly follow the derivation procedures and proofs. It has to be mentioned that, in [26,27], Hilbert's-type inequalities are studied for multiple series, applying the same approach; in addition, consult [28] for another approach to multiple Hilbert's inequalites.…”

Section: Introductionmentioning

confidence: 99%

Hilbert’s Double Series Theorem’s Extensions via the Mathieu Series Approach

Pogány

2022

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The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are the focus of a recent survey article. The sharp version of double series inequality result is extended in the case of a not exhaustively investigated non-homogeneous kernel, which mutually covers the homogeneous kernel cases as well. Particularly, novel Hilbert’s double series inequality results are presented, which include the upper bounds built exclusively with non-weighted ℓp–norms. The main mathematical tools are the integral expression of Mathieu (a, λ)-series, the Hölder inequality and a generalization of the double series theorem by Yang.

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Section: Introductionmentioning

confidence: 99%

Hilbert’s Double Series Theorem’s Extensions via the Mathieu Series Approach

Pogány

2022

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Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications

Debnath¹,

Yang

2012

International Journal of Mathematics and Mathematical Sciences

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This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. Many particular cases of Hilbert-type inequalities are presented with numerous applications. A large number of major books and recent research papers published during 2009–2012 are included to stimulate new interest in future study and research.

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Integral expressions for Hilbert-type infinite multilinear form and related multiple Hurwitz-Lerch Zeta functions

Saxena¹,

Pogány²

2012

Journal of Interpolation and Approximation in Scientific Comput

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Discrete Multiple Hilbert Type Inequality With Non-Homogeneous Kernel

Cited by 3 publications

References 5 publications

Hilbert’s Double Series Theorem’s Extensions via the Mathieu Series Approach

Hilbert’s Double Series Theorem’s Extensions via the Mathieu Series Approach

Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications

Integral expressions for Hilbert-type infinite multilinear form and related multiple Hurwitz-Lerch Zeta functions

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