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.

Generalizations of the Landau–Hadamard inequality and inequalities for quadratic polynomials of operators

1986 ◽  
Vol 102 (1-2) ◽  
pp. 123-129
Author(s):  
Khr. N. Boyadzhiev
Keyword(s):  
Differential Expression ◽  
Second Order ◽  
Functional Inequalities ◽  
Hadamard Inequality ◽  
Quadratic Polynomials

SynopsisWe give generalizations of the Landau–Hadamard inequality ‖u′‖2 ≦ K ‖u‖ ‖u″‖ replacing u” by the second-order differential expression u″ − (α + β)u′ + αβu (α, β ∈ ℂ). The new functional inequalities are then used to obtain similar inequalities for dissipative and skew-Hermitian operators.

scholarly journals Some Inequalities Using Generalized Convex Functions in Quantum Analysis

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1402 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Quantum Calculus ◽  
Quantum Analysis ◽  
Real Functions ◽  
Definition Of

In the present work, the Hermite–Hadamard inequality is established in the setting of quantum calculus for a generalized class of convex functions depending on three parameters: a number in ( 0 , 1 ] and two arbitrary real functions defined on [ 0 , 1 ] . From the proven results, various inequalities of the same type are deduced for other types of generalized convex functions and the methodology used reveals, in a sense, a symmetric mathematical phenomenon. In addition, the definition of dominated convex functions with respect to the generalized class of convex functions aforementioned is introduced, and some integral inequalities are established.

scholarly journals The stability problem of the Hermite-Hadamard inequality

2007 ◽  
pp. 359-363
Author(s):  
Kazimierz Nikodem ◽  
Thomas Riedel ◽  
Prasanna K. Sahoo
Keyword(s):  
Stability Problem ◽  
Hadamard Inequality ◽  
The Stability

scholarly journals Approximate Derivations with the Radical Ranges of Noncommutative Banach Algebras

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Jaiok Roh ◽  
Ick-Soon Chang
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Functional Inequalities ◽  
The Stability

We consider the derivations on noncommutative Banach algebras, and we will first study the conditions for a derivation on noncommutative Banach algebra. Then, we examine the stability of functional inequalities with a derivation. Finally, we take the derivations with the radical ranges on noncommutative Banach algebras.

scholarly journals Implicit Difference Inequalities Corresponding to First-Order Partial Differential Functional Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-18
Author(s):  
Z. Kamont ◽  
K. Kropielnicka
Keyword(s):  
Functional Equations ◽  
Classical Solutions ◽  
Functional Inequalities ◽  
Partial Differential ◽  
First Order ◽  
Mixed Problems ◽  
Implicit Difference Schemes ◽  
Difference Methods ◽  
The Stability ◽  
Comparison Technique

We give a theorem on implicit difference functional inequalities generated by mixed problems for nonlinear systems of first-order partial differential functional equations. We apply this result in the investigations of the stability of difference methods. Classical solutions of mixed problems are approximated in the paper by solutions of suitable implicit difference schemes. The proof of the convergence of difference method is based on comparison technique, and the result on difference functional inequalities is used. Numerical examples are presented.

scholarly journals About the Stability and Positivity of a Class of Discrete Nonlinear Systems of Difference Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Stability Conditions ◽  
Nonlinear Difference Equations ◽  
Real Functions ◽  
The Stability ◽  
Discrete Nonlinear Systems

This paper investigates stability conditions and positivity of the solutions of a coupled set of nonlinear difference equations under very generic conditions of the nonlinear real functions which are assumed to be bounded from below and nondecreasing. Furthermore, they are assumed to be linearly upper bounded for sufficiently large values of their arguments. These hypotheses have been stated in 2007 to study the conditions permanence.

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