Results 171 to 180 of about 485,864 (198)

A Generalized Gronwall-Bellman Inequality

Siberian Mathematical Journal, 2020
In 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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Gronwall Type Inequalities

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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Weakly Singular Discrete Gronwall Inequalities

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1986
Abstract Generalizations 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. This work is motivated by convergence studies of discretization methods
Dixon, J., McKee, S.
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On discrete inequalities related to Gronwall’s inequality

Proceedings of the Indian Academy of Sciences - Section A, 1977
The paper presents some new discrete inequalities related to the Well-known inequality due to Gronwall. The inequalities proved can be used in the theory of finite difference equations as handy tools.
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Nonlinear Gronwall–Bellman Type Inequalities and Their Applications [PDF]

Mathematics, 2017
In this paper, some nonlinear Gronwall–Bellman type inequalities are established. Then, the obtained results are applied to study the Hyers–Ulam stability of a fractional differential equation and the boundedness of solutions to an integral equation, respectively.
Yuqiang Feng
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Analogues of Gronwall’s inequality

1992
In this chapter we consider various analogues of Gronwall-type inequalities. These are effective tools in the study of equations of various classes.
Drumi Bainov, Pavel Simeonov
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Generalizations of Gronwall-Bellman-Reid inequalities

Applied Mathematics and Computation, 1991
In 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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On some nonlinear generalizations of Gronwall’s inequality

Proceedings of the Indian Academy of Sciences - Section A, 1976
Some useful nonlinear generalizations of the Gronwall’s inequality which contain, as special cases, the recent generalizations of this inequality given by I. Bihari, D. Willett and J. S. W. Wong and several recent works are presented.
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More Generalised Discrete Gronwall Inequalities

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1985
AbstractThe 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 ...
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Gronwall–Bellman Type Inequalities

2021
In mathematics, an integro-differential equation is an equation that covers various aspect of integrals and derivatives of an unknown function. Integral inequality act as an important role in the study of differential, integral and partial differential equations and have been of great use to Gronwall inequality.In succession to our earlier work, we ...
Apanpa, Kemi Iyabo, Rauf, Kamilu, Olaide, Oladipo Ebenezer   +2 more
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