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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.
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On a Stieltjes version of Gronwall’s inequality [PDF]
Proceedings of the American Mathematical Society, 1981 A unified formulation of Gronwall’s inequality ( GI )
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A Linear Generalization of Gronwall's Inequality [PDF]
Proceedings of the American Mathematical Society, 1965 where k(t, s) and w0(t) are known non-negative functions and u(t) is an unknown non-negative function. For examples, one can refer to Bellman [l, pp. 35 ff.], Coddington and Levinson [2, pp. 37 ff.], Willett [3], and others. In order to obtain from (1.1) a genuine upper bound for u(t), i.e., an upper bound independent of u, it seems necessary to ...
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A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator [PDF]
, 2020 In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the psi-Hilfer fractional derivative and the existence ...
Da Costa Sousa, Jose Vanterler +1 more
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Several Inequalities of Gronwall and Their Proofs [PDF]
, 2022 It is well known that integral inequalities play a very important role in studying the properties of solutions to ordinary differential equations and integral equations. In 1919, Gronwall established a class of basic integral inequalities when he studied
Wang, Xueqing; Liaoning University of International Business and Economics
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A Gronwall-type Trigonometric Inequality [PDF]
The American Mathematical Monthly, 2018 We prove that the absolute value of the $n$th derivative of $\cos(\sqrt{x})$ does not exceed $n!/(2n)!$ for all $x>0$ and $n = 0,1,\ldots$ and obtain a natural generalization of this inequality involving the analytic continuation of $\cos(\sqrt{x})$.
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On the Hyers-Ulam Stability of Differential Equations of Second Order
Abstract and Applied Analysis, 2014 By using of the Gronwall inequality, we prove the Hyers-Ulam stability of differential equations of second order with initial conditions.
Qusuay H. Alqifiary, Soon-Mo Jung
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Robust finite-time stability of neutral fractional time-delay systems
上海师范大学学报. 自然科学版, 2020 This paper is devoted to investigating the robust finite-time stability issue of neutral fractionalorder system. Based on the generalized Bellman-Gronwall inequality, a new sufficient condition is established for the particular class of neutral ...
ZHANG Li, GAO Cunchen, REN Qifeng
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Remark on Gronwall’s inequality
Proceedings Mathematical Sciences, 1992 The present note is devoted to abstract analogues of the Gronwall inequality in classical propositional calculus. Let \(a_ 1,a_ 2,\dots,b_ 1,b_ 2,\dots,\) and \(x_ 1,x_ 2,\dots\) be infinite sets of statement variables and \(\sim\), \(\land\), \(\lor\), \(\supset\), and \(\equiv\) connectives in classical propositional calculus. The main results of the
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A new approach to interval-valued inequalities
Advances in Difference Equations, 2020 The objective of this work is to advance and simplify the notion of Gronwall’s inequality. By using an efficient partial order and concept of gH-differentiability on interval-valued functions, we investigate some new variants of Gronwall type ...
Awais Younus +4 more
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