scholarly journals A refined discrete Hilbert inequality obtained via the Hermite–Hadamard inequality

2012 ◽  
Vol 63 (12) ◽  
pp. 1587-1596 ◽  
Author(s):  
Mario Krnić
Keyword(s):  
Hilbert Inequality ◽  
Hadamard Inequality

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.

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.

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.

scholarly journals Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Quantum Calculation ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Quantum Integral

In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

scholarly journals Some Properties and Inequalities for the h,s-Nonconvex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chengli Wang ◽  
Muhammad Shoaib Saleem ◽  
Hamood Ur Rehman ◽  
Muhammad Imran
Keyword(s):  
Jensen Inequality ◽  
Weighted Version ◽  
Hadamard Inequality ◽  
Basic Properties ◽  
Nonconvex Functions ◽  
Schur Inequality ◽  
Class Of Functions

The purpose of this paper is to introduce the notion of strongly h,s-nonconvex functions and to present some basic properties of this class of functions. We present Schur inequality, Jensen inequality, Hermite–Hadamard inequality, and weighted version of the Hermite–Hadamard inequality.

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