On an Extension of Hilbert Inequality

2012 ◽  
Vol 166-169 ◽  
pp. 3023-3026
Author(s):  
Bao Ju Sun
Keyword(s):  
Cauchy Inequality ◽  
Hilbert Inequality ◽  
Hadamard Inequality

In this paper, by using Hadamard inequality and Cauchy inequality, an extension of Hilbert inequality is established.

scholarly journals On Hilbert's Inequality for Double Series and Its Applications

2008 ◽  
Vol 2008 ◽  
pp. 1-12
Author(s):  
Zhou Yu ◽  
Gao Mingzhe
Keyword(s):  
Real Function ◽  
Hardy Inequality ◽  
Double Series ◽  
Cauchy Inequality ◽  
Hilbert Inequality ◽  
Hilbert’S Inequality ◽  
Riesz Inequality

This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real functionu(x)and a parameterλ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHpfunction are given.

On a certain stability of the Hermite–Hadamard inequality

2008 ◽  
Vol 465 (2102) ◽  
pp. 571-583 ◽  
Author(s):  
Attila Házy ◽  
Zsolt Páles
Keyword(s):  
Functional Inequalities ◽  
Hadamard Inequality ◽  
Real Functions ◽  
The Stability

The classical Hermite–Hadamard inequality, under some regularity assumptions, characterizes convexity of real functions. The aim of this paper is to establish connections between the stability forms of the functional inequalities related to Jensen convexity, convexity and the Hermite–Hadamard inequality.

On a Refinement of Hardy-Hilbert Inequality

2012 ◽  
Vol 166-169 ◽  
pp. 3027-3030
Author(s):  
Bao Ju Sun
Keyword(s):  
Weight Coefficient ◽  
Hilbert Inequality ◽  
Maximum Minimum

In this paper, by using Maximum-minimum monotonic theorem and estimating the weight coefficient, a refinement of Hardy- Hilbert inequality is established.

Sharpening of Cauchy Inequality

1998 ◽  
pp. 485-487
Author(s):  
Živojin Mijalković ◽  
Milan Mijalković
Keyword(s):  
Cauchy Inequality

scholarly journals New Hermite–Hadamard Type Inequalities Involving Non-Conformable Integral Operators

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1108 ◽  
Author(s):  
Juan E. Nápoles Valdés ◽  
José M. Rodríguez ◽  
José M. Sigarreta
Keyword(s):  
Integral Operators ◽  
Hadamard Inequality ◽  
Applied Development

At present, inequalities have reached an outstanding theoretical and applied development and they are the methodological base of many mathematical processes. In particular, Hermite– Hadamard inequality has received considerable attention. In this paper, we prove some new results related to Hermite–Hadamard inequality via symmetric non-conformable integral operators.

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