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An Extension of the Fractional Gronwall Inequality
2019published
Ricardo Almeida +2 more
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Sharp generalizations of stochastic Gronwall inequalities
2023In dieser Arbeit betrachten wir zwei stochastische Ungleichungen, welche miteinander zusammenhängen: Eine Ungleichung von Lenglart (1977) und eine Klasse stochastischer Gronwall-Ungleichungen, die von Renesse und Scheutzow (2010), Scheutzow (2013), Xie und Zhang (2020) und Mehri und Scheutzow (2021) studiert wurden.
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An extension of Gronwall's inequality
2020One of the results in this paper is the extended Gronwall's inequality. Theorem: Let \(k\geq 1\) be an integer. Suppose that \[ \varphi^k(t)\leq c_0^k(t)+ \int_0^t [kc_1(s)+ kc_2(s) \varphi^2(s)+\dots+ kc_k(s) \varphi^k(s)] ds \] for a.e. \(t\in[0,T]\), where \(c_0\geq 0\) is nonincreasing, \(\varphi\in L^\infty\) and \(\varphi\geq 0\) for a.e. \(t\in [
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Discrete Gronwall inequalities in many variables
, 1999J. Popenda, R. Agarwal
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Further Nonlinear Retarded Integral Inequalities for Gronwall–Bellman Type and Their Applications
Iranian Journal of Science and Technology, Transactions A: Science, 2019A. Shakoor +4 more
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New Henry–Gronwall Integral Inequalities and Their Applications to Fractional Differential Equations
, 2018Tao Zhu
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A Variety of Nonlinear Retarded Integral Inequalities of Gronwall Type and Their Applications
, 2018A. El-Deeb
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