Some nonlinear weakly singular integral inequalities with two variables and applications.

Wang, Hong; Zheng, Kelong

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Two-point boundary value problems for higher-order linear differential equations with strong singularities.

Agarwal, R.P., Kiguradze, I. (2006)

Boundary Value Problems [electronic only]

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On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.

Chen, Lian-Ying, Zhao, Chang-Jian, Cheung, Wing-Sum (2010)

Journal of Inequalities and Applications [electronic only]

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Inequalities for the Riemann–Stieltjes Integral of under the Chord Functions with Applications

Silvestru S. Dragomir (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We say that the function $f : [a, b] \to ℝ$ is under the chord if $\frac{(b - t) f (a) + (t - a) f (b)}{b - a} \geq f (t)$ for any $t \in [a, b]$ . In this paper we proved amongst other that $\int_{a}^{b} u (t) d f (t) \geq \frac{f (b) - f (a)}{b - a} \int_{a}^{b} u (t) d t$ provided that $u : [a, b] \to ℝ$ is monotonic nondecreasing and $f : [a, b] \to ℝ$ is continuous and under the chord. Some particular cases for the weighted integrals in connection with the Fejér inequalities are provided. Applications for continuous functions of selfadjoint operators on Hilbert spaces are also given.