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On hierarchical competition through reduction of individual growth. [PDF]
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Weakly Singular Discrete Gronwall Inequalities
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1986AbstractGeneralizations of the classical Gronwall inequality when the kernel of the associated integral equation is weakly singular are presented. The continuous and discrete versions are both given; the former is included since it suggests the latter by analogy.
J. Dixon, S. McKee
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More Generalised Discrete Gronwall Inequalities
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1985AbstractThe most general linear discrete Gronwall inequality is first considered, and best possible solutions of the inequality are obtained by elementary methods which are discrete analgoues of those used for Volterra integral equations. Upper bounds are also obtained for solutions in case the kernel is of a generalised Abel type, improving and ...
P. Beesack
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Stochastic version of Henry type Gronwall’s inequality
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2021We use Young’s and Hölder inequality combined with classical Gronwall’s inequality to derive present a new version of the stochastic of Gronwall’s inequalities with singular kernels.
Mekki, Slimane +2 more
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Rocky Mountain Journal of Mathematics, 2021
We propose and prove some new generalized Gronwall-type inequalities with respect to an appropriate function ψ. We consider the integral inequalities including not only one integral but also two integrals with doubly singular kernels.
M. Nguyen
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We propose and prove some new generalized Gronwall-type inequalities with respect to an appropriate function ψ. We consider the integral inequalities including not only one integral but also two integrals with doubly singular kernels.
M. Nguyen
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Gronwall Inequalities in Higher Dimensions
, 1991Several authors generalized inequalities of Gronwall type to the case of functions of two or more variables. Of course, such results have application in the theory of partial differential equations and Volterra integral equations.
D. S. Mitrinovic +2 more
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A Generalized Gronwall-Bellman Inequality
Siberian Mathematical Journal, 2020In this paper, some Gronwall-Bellman-type integral inequalities in which the argument of the exponent depends linearly on \(N\). Specifically, the following result is established: Let \(u(x)\), \(A(x)\) be nonnegatine continuous functions on \([0,x_0]\) satisfies \[ u(x) \le A + N\int^{x}_{0}P_m(N(x-\zeta))u(\zeta)d\zeta,\; x\in [0,x_0],\, x_0>0 ...
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SIAM Journal on Numerical Analysis
We consider the completely positive discretizations of fractional ordinary differential equations (FODEs) on nonuniform meshes. Making use of the resolvents for nonuniform meshes, we first establish comparison principles for the discretizations.
Yuanyuan Feng +3 more
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We consider the completely positive discretizations of fractional ordinary differential equations (FODEs) on nonuniform meshes. Making use of the resolvents for nonuniform meshes, we first establish comparison principles for the discretizations.
Yuanyuan Feng +3 more
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Generalizations of Gronwall-Bellman-Reid inequalities
Applied Mathematics and Computation, 1991In the paper, the authors consider some one-variable linear and nonlinear integral inequalities of the Gronwall-type. Some linear inequalities involving iterated integral functionals are discussed in the first three theorems, which are all special cases of an inequality considered by this reviewer [J. Math. Anal. Appl.
Zaghrout, A. A. S., El-Dawaliby, N.
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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1995
AbstractIn Abschnitt I werden verschiedene Formen derjenigen Integralungleichung betrachtet, die von vielen Autoren als Gronwall‐Ungleichung beschrieben wird, und es wird versucht, eine allgemeine Definition zu geben. In Abschnitt II wird eine algebraische Version gegeben, von der gezeigt wird, daß sich daraus viele der bekannten Gronwall‐Ungleichungen
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AbstractIn Abschnitt I werden verschiedene Formen derjenigen Integralungleichung betrachtet, die von vielen Autoren als Gronwall‐Ungleichung beschrieben wird, und es wird versucht, eine allgemeine Definition zu geben. In Abschnitt II wird eine algebraische Version gegeben, von der gezeigt wird, daß sich daraus viele der bekannten Gronwall‐Ungleichungen
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