给出了一类积分项外包含非常数项的非线性弱奇异迭代积分不等式,并利用离散Jensen不等式、Hlder积分不等式、变量替换技巧和放大技巧等分析手段给出了该非线性弱奇异迭代积分不等式中未知函数的上界估计,最后举例说明所得估计可以用来研究分数阶积分方程解的定性性质.
A class of nonlinear weakly singular iterated integral inequalities is given.There is a nonconstant term outside the integrals in the integral inequality.The upper bound of the embedded unknown function of the inequalities is estimated explicitly by adopting novel analysis techniques, such as: discrete Jensen inequality, H(o)lder integral inequality, the techniques of change of variable, and the method of amplification.The derived results can be applied in the study of qualitative properties of solutions of fractional integral equations.