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Repeated Integral Inequalities

IMA Journal of Numerical Analysis, 1984
The purpose of this paper is to present the following linear generalization of Gronwall's inequality: Let the function x be continuous and non-negative on the interval [0,T]. If \[ x(t)\leq \Phi (t)+M\int^{t}_{0}\int^{t_ m}_{0}...\int^{t_ 1}_{0}[x(s)/(t_ 1-s)^{\alpha}]ds dt_ 1...dt_ m,\quad t\in [0,T], \] where \(\alpha 0\) is constant, and \(\Phi\) (t)
Dixon, Jennifer, McKee, Sean
openaire   +2 more sources

Generalized integral Niezgoda’s inequalities

Asian-European Journal of Mathematics, 2022
In this paper, we give generalizations followed by refinements of the integral version of Niezgoda’s inequality in several different ways by using weights, functions with nondecreasing increments and isotonic linear functionals.
M. Maqsood Ali, Asif R. Khan
openaire   +1 more source

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