scholarly journals A New Multinomial Nonlinear Integral Inequality Involving a Generalization of the Bihari Type Inequality

1994 ◽  
Vol 184 (3) ◽  
pp. 464-471
Author(s):  
H.Z. Xie
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Nonlinear Integral Inequality

scholarly journals New Integral Inequalities via Generalized Preinvex Functions

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 296
Author(s):  
Muhammad Tariq ◽  
Asif Ali Shaikh ◽  
Soubhagya Kumar Sahoo ◽  
Hijaz Ahmad ◽  
Thanin Sitthiwirattham ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Power Mean ◽  
Science And Engineering ◽  
Special Means ◽  
Algebraic Properties ◽  
Convexity Theory ◽  
Hölder’S Integral Inequality ◽  
Preinvex Functions

The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex function and to present inequalities of the Hermite–Hadamard type in the setting of the generalized s-type m–preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite–Hadamard-type inequality using Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory.

scholarly journals A reverse Hilbert-type inequality with a generalized homogeneous kernel

2011 ◽  
Vol 42 (1) ◽  
pp. 1-7
Author(s):  
Bing He
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Homogeneous Kernel ◽  
Best Constant ◽  
Type Integral ◽  
Best Constant Factor ◽  
Hilbert Type

Inthispaper,by introducing a generalized homogeneous kernel and estimating the weight function,a new reverse Hilbert-type integral inequality with some parameters and a best constant factor is established.Furthermore, the corresponding equivalent form is considered.

scholarly journals A general Ostrowski type inequality for double integrals

2002 ◽  
Vol 33 (4) ◽  
pp. 319-334
Author(s):  
G. Hanna ◽  
S. S. Dragomir ◽  
P. Cerone
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Two Dimensions ◽  
One Dimensional ◽  
Ostrowski Type Inequality ◽  
And Function ◽  
Interior Points ◽  
Double Integrals ◽  
Differentiable Mappings

Some generalisations of an Ostrowski Type Inequality in two dimensions for $n-$time differentiable mappings are given. The result is an Integral Inequality with bounded $n-$time derivatives. This is employed to approximate double integrals using one dimensional integrals and function evaluations at the boundary and interior points.

scholarly journals Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jianquan Liao ◽  
Yong Hong ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Multiple Integral ◽  
Constant Factor ◽  
Weight Functions ◽  
Homogeneous Kernel ◽  
Optimal Constant ◽  
Equivalent Parameter ◽  
Parameter Condition ◽  
Hilbert Type

Let ∑i=1n1/pi=1pi>1, in this paper, by using the method of weight functions and technique of real analysis; it is proved that the equivalent parameter condition for the validity of multiple integral Hilbert-type inequality ∫R+nKx1,⋯,xn∏i=1nfixi dx1⋯dxn≤M∏i=1nfipi,αi with homogeneous kernel Kx1,⋯,xn of order λ is ∑i=1nαi/pi=λ+n−1, and the calculation formula of its optimal constant factor is obtained. The basic theory and method of constructing a Hilbert-type multiple integral inequality with the homogeneous kernel and optimal constant factor are solved.

scholarly journals On a Generalization of Hilbert-Type Integral Inequality

2008 ◽  
Vol 2008 ◽  
pp. 1-8
Author(s):  
Sun Baoju
Keyword(s):  
Integral Inequality ◽  
Equivalent Form ◽  
Type Inequality ◽  
Type Integral ◽  
Hilbert Type

By introducing some parameters, we establish generalizations of the Hilbert-type inequality. As applications, the reverse and its equivalent form are considered.

A Multidimensional Integral Inequality Related to Hilbert-Type Inequality

2016 ◽  
Vol 13 (6) ◽  
pp. 3837-3848
Author(s):  
Vandanjav Adiyasuren ◽  
Tserendorj Batbold ◽  
Yoshihiro Sawano
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Multidimensional Integral ◽  
Hilbert Type

Upper and Lower Bounds of Unknown Functions in Several Nonlinear Integral Inequalities in Engineering

2014 ◽  
Vol 1008-1009 ◽  
pp. 1517-1520
Author(s):  
Li Mian Zhao ◽  
Ji Ting Huang ◽  
Wu Sheng Wang
Keyword(s):  
Lower Bounds ◽  
Integral Inequality ◽  
Unknown Function ◽  
Integral Inequalities ◽  
Upper And Lower Bounds ◽  
Nonlinear Integral Inequality ◽  
Amplification Method ◽  
Lower Estimation ◽  
Change Of Variable ◽  
Linear Integral

In this paper, we discuss the upper and lower bounds of unknown functions in several nonlinear integral inequalities. Firstly, we give out the upper estimation of unknown function of a nonlinear integral inequality. Secondly, we give out the lower estimation of unknown function of another nonlinear integral inequality. Finally, we discuss the upper and lower bounds of a linear integral inequality by adopting novel analysis techniques, such as change of variable, amplification method, differential and integration.

A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation

2020 ◽  
Vol 21 (7-8) ◽  
pp. 667-673
Author(s):  
Mohammad Wajeeh Alomari
Keyword(s):  
Bounded Variation ◽  
Integral Inequality ◽  
Type Inequality ◽  
Quadrature Rule ◽  
Ostrowski Type Inequality

AbstractA weighted companion of Ostrowski type inequality is established. Some sharp inequalities are proved. Application to a quadrature rule is provided.

scholarly journals On refinements of some integral inequalities for differentiable prequasiinvex functions

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4377-4385
Author(s):  
Serap Özcan
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Right Hand ◽  
The Right ◽  
New Inequalities ◽  
Better Than

In this paper, using the new and improved form of H?lder?s integral inequality called H?lder-??can integral inequality, some new inequalities of the right-hand side of Hermite-Hadamard type inequality for prequasiinvex functions are established. The results obtained are compared with the known results. It is shown that the results obtained in this paper are better than those known ones.

scholarly journals Nonlinear Inequalities with Double Riesz Potentials

2021 ◽  
Author(s):  
Marius Ghergu ◽  
Zeng Liu ◽  
Yasuhito Miyamoto ◽  
Vitaly Moroz
Keyword(s):  
Integral Inequality ◽  
Riesz Potentials ◽  
Nonlinear Integral Inequality ◽  
Optimal Decay ◽  
Nonnegative Solutions

AbstractWe investigate the nonnegative solutions to the nonlinear integral inequality u ≥ Iα ∗((Iβ ∗ up)uq) a.e. in ${\mathbb R}^{N}$ ℝ N , where α, β ∈ (0, N), p, q > 0 and Iα, Iβ denote the Riesz potentials of order α and β respectively. Our approach relies on a nonlocal positivity principle which allows us to derive optimal ranges for the parameters α, β, p and q to describe the existence and the nonexistence of a solution. The optimal decay at infinity for such solutions is also discussed.

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