[PDF] Top 20 On Hilbert type inequalities

... In recent years several authors have given considerable attention to Hilbert’s double-series inequality together with its integral version, inverse version, and various generalizations (see [–]). In this paper, we ... See full document

... Motivated by some recent results, in this paper we derive several half-discrete Hilbert-type inequalities with a homogeneous kernel involving some differential operators. The main results are proved ... See full document

... decades, Hilbert-type inequalities (1) and (2) have been extensively studied by numerous ...included inequalities with more general kernels, weight functions, and integration domains, as well ... See full document

... to Hilbert inequalities and Hilbert-type inequalities and their various generalizations by several authors including Handley et ...integral inequalities similar to Hilbert ... See full document

... On reverse Hilbert-type inequalities Biao Xu1* , Xu-Huan Wang2 , Wei Wei3 and Haoxiang Wang4 * Correspondence: [email protected] 1 School of Mathematical Science, Huaibei Normal Universi[r] ... See full document

... For some particular types of functions of k(x, y) (adding as well some conditions upon (2.3) and (2.5)), we obtain some classical Hilbert-type inequalities as follows: (i) For k(x, y) = x+y 1 , since ... See full document

... to Hilbert-type ...the Hilbert-type ...of inequalities () and () was solved in  by introducing two pairs of conjugate ... See full document

... We consider the Hilbert-type inequalities with nonconjugate parameters. The obtaining of the best possible constants in the case of nonconjugate parameters remains still open. Our generalization will ... See full document

... Hardy-Hilbert type inequalities see 1 are very significant weight inequalities which play an important role in many fields of ...such inequalities have attracted the interest of ... See full document

... By means of the weight coefficients and the idea of introducing parameters, a discrete Hilbert-type inequality with the general homogeneous kernel and the intermediate variables is given. The equivalent form ... See full document

... a Hilbert-type linear operator with a symmetric homogeneous kernel, one can obtain var- ious Hilbert-type inequalities with the best constant ... See full document

... half-discrete Hilbert-type in- equalities with particular ...integral Hilbert-type inequalities with some additional conditions on the kernel, a half-discrete Hilbert-type ... See full document

... of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and ...of Hilbert-type inequalities involving many special functions such as beta, ... See full document

... analysis and their applications cf. 3. In near one century, there are many improvements, generalizations and, applications of 1.1–1.4 in numerous literatures and monographs of mathematics cf. 2–18. Yang and Huang also ... See full document

... of Hilbert-type inequalities with the homogeneous kernels of negative num- ber degrees was given by ...some inequalities with the homogeneous kernels of degree  and non-homogeneous kernels ... See full document

... It is known, see for instance [9, p. 356-358], that if A and B are two commuting bounded selfadjoint operators on the complex Hilbert space H, then there exists a bounded selfadjoint operator S on H and two ... See full document

... 2. A Version of the ˇ Cebyˇ sev Inequality for One Operator Let A be a selfadjoint linear operator on a complex Hilbert space (H; h., .i) . The Gelfand map establishes a ∗-isometrically isomorphism Φ between the ... See full document

... Proposition 1 Let A be a selfadjoint operator on the Hilbert space H and assume that Sp (A) ⊆ [m, M] for some scalars m, M with 0 < m < M. If f is a continuously differentiable convex function on [m, M] with ... See full document

... Dragomir, Reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces.. Fink, A treatise on Grüss’ inequality, Analytic and Geometric Inequal[r] ... See full document

... Theorem 2 (Dragomir, 2008, [17]). Let A be a selfadjoint operator on the Hilbert space (H, h., .i) with the spectrum Sp (A) ⊆ [m, M] for some real numbers m < M. If f, g : [m, M ] −→ R are continuous and ... See full document