Some generalizations of the Hermite–Hadamard integral inequality

AbstractIn this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity property of the target function is not assumed in advance. They represent a refinement of this inequality in the case of convex/concave functions with numerous applications.

Download Full-text

Some Generalizations of Jensen's Inequality

Contemporary Mathematics ◽

10.37256/cm.212021686 ◽

2020 ◽

Author(s):

Slavko Simic ◽

Bandar Almohsen

Keyword(s):

Target Function ◽

Jensen’S Inequality ◽

Convexity Property ◽

Concave Functions ◽

Jensen's Inequality ◽

Differentiable Functions ◽

Probability And Statistics

In this article, we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They represent a refinement of these inequalities in the case of convex/concave functions with numerous applications in Theory of Means and Probability and Statistics.

Download Full-text

Simpson’s Rule and Hermite–Hadamard Inequality for Non-Convex Functions

Mathematics ◽

10.3390/math8081248 ◽

2020 ◽

Vol 8 (8) ◽

pp. 1248

Author(s):

Slavko Simić ◽

Bandar Bin-Mohsin

Keyword(s):

Integral Inequality ◽

Convex Functions ◽

Concave Functions ◽

Hadamard Inequality ◽

Differentiable Functions ◽

Simpson’S Rule ◽

Simpson's Rule

In this article we give a variant of the Hermite–Hadamard integral inequality for twice differentiable functions. It represents an improvement of this inequality in the case of convex/concave functions. Sharp two-sided inequalities for Simpson’s rule are also proven along with several extensions.

Download Full-text

An integral inequality for differentiable functions of several variables

Siberian Mathematical Journal ◽

10.1007/bf00968694 ◽

1985 ◽

Vol 25 (5) ◽

pp. 790-794 ◽

Cited By ~ 1

Author(s):

Yu. G. Reshetnyak

Keyword(s):

Integral Inequality ◽

Differentiable Functions ◽

Several Variables

Download Full-text

General Raina fractional integral inequalities on coordinates of convex functions

Advances in Difference Equations ◽

10.1186/s13662-021-03241-y ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Dumitru Baleanu ◽

Artion Kashuri ◽

Pshtiwan Othman Mohammed ◽

Badreddine Meftah

Keyword(s):

Mathematical Model ◽

Fractional Calculus ◽

Convex Function ◽

Mathematical Analysis ◽

Integral Inequality ◽

Convex Functions ◽

Fractional Integral ◽

Integral Inequalities ◽

Differentiable Functions ◽

Special Cases

AbstractIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the $(l_{1},h_{1})$ ( l 1 , h 1 ) -$(l_{2},h_{2})$ ( l 2 , h 2 ) -convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.

Download Full-text

INTEGRAL INEQUALITY REGARDING γ-CONVEX AND γ-CONCAVE FUNCTIONS

Journal of the Korean Mathematical Society ◽

10.4134/jkms.2010.47.2.373 ◽

2010 ◽

Vol 47 (2) ◽

pp. 373-383

Author(s):

WaadAllah T. Sulaiman

Keyword(s):

Integral Inequality ◽

Concave Functions

Download Full-text

ON AN INTEGRAL INEQUALITY OF R. BELLMAN

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.22.1991.4597 ◽

1991 ◽

Vol 22 (2) ◽

pp. 187-191

Author(s):

HORST ALZER

Keyword(s):

Integral Inequality ◽

Concave Functions

We prove: if $u$ and $v$ are non-negative, concave functions defined on $[0, 1]$ satisfying \[\int_0^1 (u(x))^{2p} dx =\int_0^1 (v(x))^{2q} dx=1, \quad p>0, \quad q>0,\] then \[\int_0^1(u(x))^p (v(x))^q dx\ge\frac{2\sqrt{(2p+1)(2q+1)}}{(p+1)(q+1)}-1.\]

Download Full-text

NOTE ON AN INTEGRAL INEQUALITY FOR CONCAVE FUNCTIONS

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.27.1996.4354 ◽

1996 ◽

Vol 27 (2) ◽

pp. 161-163

Author(s):

HORST ALZER

Keyword(s):

Integral Inequality ◽

Concave Functions

We prove: Let $p\in C^2[a, b]$ be non-negative and concave, and let $f\in C^2[a, b]$ with $f(a)=f(b)=0$. Then \[ \left(\int_a^b p(x)(f'(x))^2 dx\right)^2\le \left(\int_a^b p(x)(f(x))^2 dx\right)\left(\int_a^b p(x)(f''(x))^2 dx\right) .\] Moreover, we determine all cases of equality.

Download Full-text

Modeling And Optimization Of The Construction Organization's Production Program

Promyshlennoe i Grazhdanskoe Stroitel stvo ◽

10.33622/0869-7019.2020.06.49-56 ◽

2020 ◽

pp. 49-56

Keyword(s):

Software Package ◽

Target Function ◽

Optimization Models ◽

Labor Resource ◽

Production Program ◽

Construction Organizations ◽

Source Data ◽

Labor Resources ◽

Construction Organization ◽

Planning Production

In the article, the author considers the problems of complex algorithmization and systematization of approaches to optimizing the work plans of construction organizations (calendar plans) using various modern tools, including, for example, evolutionary algorithms for "conscious" enumeration of options for solving a target function from an array of possible constraints for a given nomenclature. Various typical schemes for modeling the processes of distribution of labor resources between objects of the production program are given, taking into account the array of source data. This data includes the possibility of using the material and technical supply base (delivery, storage, packaging) as a temporary container for placing the labor resource in case of released capacity, quantitative and qualification composition of the initial labor resource, the properties of the construction organization as a counterparty in the contract system with the customer of construction and installation works etc. A conceptual algorithm is formed that is the basis of the software package for operational harmonization of the production program ( work plans) in accordance with the loading of production units, the released capacities of labor resources and other conditions stipulated by the model. The application of the proposed algorithm is most convenient for a set of objects, which determines the relevance of its implementation in optimization models when planning production programs of building organizations that contain several objects distributed over a time scale.

Download Full-text