A Class of Nonlinear Weakly Singularity Wendroff Type Integral Inequality with Two Variables and Application

2014 ◽  
Vol 1008-1009 ◽  
pp. 1493-1496
Author(s):  
Wu Sheng Wang ◽  
Yi Bing Lai
Keyword(s):  
Integral Inequality ◽  
Unknown Function ◽  
Nonlinear Function ◽  
Jensen Inequality ◽  
Composite Function ◽  
Type Integral

In this paper, we establish a nonlinear weakly singularity Wendroff type integral inequality with two variables, which generalizes the unknown function with a variable to composite function of nonlinear function with unknown function with two variables. Under certain conditions, the estimation of unknown function is given by the technique of amplification, variable substitutions, integration and differentiation, discrete Jensen inequality.

scholarly journals A Multiple Iterated Integral Inequality and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zongyi Hou ◽  
Wu-Sheng Wang
Keyword(s):  
Unknown Function ◽  
Nonlinear Function ◽  
Integral Inequalities ◽  
Nonlinear Functions ◽  
Fredholm Type ◽  
Composite Function ◽  
Analysis Techniques ◽  
Nonlinear Anal ◽  
Type Integral ◽  
Iterated Integral

We establish new multiple iterated Volterra-Fredholm type integral inequalities, where the composite functionw(u(s))of the unknown functionuwith nonlinear functionwin integral functions in [Ma, QH, Pečarić, J: Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities.Nonlinear Anal.69 (2008) 393–407] is changed into the composite functionsw1(u(s)),w2(u(s)),…, wn (u(s))of the unknown functionuwith different nonlinear functionsw1,w2,…,wn, respectively. By adopting novel analysis techniques, the upper bounds of the embedded unknown functions are estimated explicitly. The derived results can be applied in the study of solutions of ordinary differential equations and integral equations.

Estimation of the Unknown Function of Integral Inequality with Power Function and its Application

2014 ◽  
Vol 1008-1009 ◽  
pp. 1505-1508
Author(s):  
Wu Sheng Wang ◽  
Tian Su
Keyword(s):  
Power Function ◽  
Integral Inequality ◽  
Unknown Function ◽  
Jensen Inequality ◽  
Composite Function ◽  
Amplification Method ◽  
Method Integration ◽  
Change Of Variable

In this paper, we establish a new weakly singularity integral inequality with two variables, which generalize the unknown function with a variable to composite function of power function with unknown function with two variables. Under certain conditions, the estimation of unknown function is given by technique of change of variable, amplification method, integration and differentiation, discrete Jensen inequality and inequality.

scholarly journals A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Jun Zhou
Keyword(s):  
Differential Equation ◽  
Initial Data ◽  
Fractional Differential Equation ◽  
Integral Inequality ◽  
Unknown Function ◽  
Continuous Dependence ◽  
Weak Singularity ◽  
Type Integral ◽  
Fractional Differential ◽  
Continuous Dependence Of Solutions

We discuss on integrable solutions for a generalized Henry-type integral inequality in which weak singularity and delays are involved. Not requiring continuity or differentiability for some given functions, we use a modified iteration argument to give an estimate of the unknown function in terms of the multiple Mittag-Leffler function. We apply the result to give continuous dependence of solutions on initial data, derivative orders, and known functions for a fractional differential equation.

scholarly journals A Generalized Nonlinear Gronwall-Bellman Inequality with Maxima in Two Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yong Yan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Integral Inequality ◽  
Unknown Function ◽  
Boundary Value ◽  
Partial Differential ◽  
Type Integral ◽  
Nonlinear Integrals ◽  
Function Of Two Variables

This paper deals with a generalized form of nonlinear retarded Gronwall-Bellman type integral inequality in which the maximum of the unknown function of two variables is involved. This form includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals. Requiring neither monotonicity nor separability of given functions, we apply a technique of monotonization to estimate the unknown function. Our result can be used to weaken conditions for some known results. We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness.

A Simons type integral inequality for closed submanifolds in the product space Sn×R

2021 ◽  
Vol 209 ◽  
pp. 112366
Author(s):  
Fábio R. dos Santos ◽  
Sylvia F. da Silva
Keyword(s):  
Integral Inequality ◽  
Product Space ◽  
Type Integral

scholarly journals A reverse Hardy–Hilbert-type integral inequality involving one derivative function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Chen ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Beta Function ◽  
Equivalent Form ◽  
Constant Factor ◽  
Weight Functions ◽  
Derivative Function ◽  
The Best Possible Constant ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

AbstractIn this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

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