Results 11 to 20 of about 606,903 (214)

Integral inequalities similar to Gronwall inequality

Electronic Journal of Differential Equations, 2007
In the present paper, we establish some nonlinear integral inequalities for functions of one variable, with a further generalization functions with n independent variables.
Hassane Khellaf, Mohamed Denche
doaj   +2 more sources

Best possible gronwall inequalities

Mathematical and Computer Modelling, 1997
The authors have obtained upper estimates on the inequalities of the form \[ u_{n+ 1}\leq T_n\{u\},\quad n= 1,2,\dots, \] by using the monotonicity of the operators involved. The mathematical induction is used to establish the results in the paper.
E. Magnucka-Blandzi, J. Popenda, R. Agarwal   +2 more
semanticscholar   +3 more sources

Gronwall inequalities via Picard operators

Annals of the Alexandru Ioan Cuza University - Mathematics, 2012
Let \(A\) be an operator on an ordered set \(X\) such that the equation \(A(x)=x\) has a unique solution \(x^\ast\). The second author raised the following problem in his study of Picard operators [Sci. Math. Jpn. 58, No. 1, 191--219 (2003; Zbl 1031.47035)]: Find the conditions under which \(x\leq A(x)\), respectively \(x\geq A(x)\), implies that \(x ...
N. Lungu, I. Rus
semanticscholar   +2 more sources

Gronwall inequalities on time scales [PDF]

Mathematical Inequalities & Applications, 2006
The authors use several different methods to extend Gronwall’s inequality to more general cases on a time scale. Two applications are also given. Mathematics subject classification (2000): 26D15.
F. Wong, Cheh-Chih Yeh, Chen-Huang Hong
semanticscholar   +2 more sources

On some Gronwall-Wendorff-type inequalities

Journal of Numerical Analysis and Approximation Theory, 1993
Not available.
Nicolae Lungu
doaj   +3 more sources

Linear generalizations of Gronwall’s inequality [PDF]

Proceedings of the American Mathematical Society, 1976
A variety of linear generalizations of Gronwall's inequality, including recent multivariable results of D. R. Snow and E. C. Young, are subsumed and extended by simple arguments involving the resolvent kernel of the integral operator.
Chandra, Jagdish, Davis, Paul W.
openaire   +2 more sources

Extensions of Gronwall-Bellman type integral inequalities with two independent variables

Open Mathematics, 2022
In this paper, we establish several kinds of integral inequalities in two independent variables, which improve well-known versions of Gronwall-Bellman inequalities and extend them to fractional integral form.
Xie Yihuai, Li Yueyang, Liu Zhenhai
doaj   +1 more source

Minimal Conditions for Implications of Gronwall-Bellman Type [PDF]

, 2016
Gronwall-Bellman type inequalities entail the following implication: if a sufficiently integrable function satisfies a certain homogeneous linear integral inequality, then it is nonpositive.
Herdegen, Martin, Herrmann, Sebastian
core   +2 more sources

Generalizations of the Nonlinear Henry Inequality and the Leray–Schauder Type Fixed Point Theorem with Applications to Fractional Differential Inclusions

Fractal and Fractional, 2021
The authors give some singular versions of the Gronwall–Bihari–Henry inequalities. They also establish a multivalued version of the Leray–Schauder alternative in strictly star-shaped sets.
Zouaoui Hamlat, John R. Graef, Abdelghani Ouahab   +2 more
doaj   +1 more source

Some dynamic inequalities on time scales and their applications

Advances in Difference Equations, 2019
This paper is devoted to the study of Gronwall–Bellman-type inequalities on an arbitrary time scale T $\mathbb{T}$. We investigate some new explicit bounds of a certain class of nonlinear retarded dynamic inequalities of Gronwall–Bellman type on time ...
A. A. El-Deeb, Haiyong Xu, A. Abdeldaim, Guotao Wang   +3 more
doaj   +1 more source