*Correspondence: [email protected] School of Science, Shandong University of Technology, Zhangzhou Road 12, Zibo, Shandong 255049, China Abstract In this paper, some new Gronwall-Bellman-type integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of qualitative and quantitative properties of solutions of dynamic equation...

The theory of the calculus of variations was recently extended to the more general time scales setting, both for delta and nabla integrals. The primary purpose of this paper is to further extend the theory on time scales, by establishing some basic diamond-alpha dynamic integral inequalities. We prove generalized versions of Hölder, Cauchy-Schwarz, Minkowski, and Jensen’s inequalities. For the ...

In the present paper we establish some integral inequalities analogous to the wellknown Hadamard inequality for a class of generalized weighted quasi-arithmetic means in integral form.

We prove some integral inequalities involving the Laplace transform. These are sharper than some known generalizations of the Hilbert integral inequality including a recent result of Yang.

The theory of fuzzy measures and fuzzy integrals was introduced by Sugeno [24] as a tool for modeling nondeterministic problems. Sugeno’s integral is analogous to Lebesgue integral which has been studied by many authors, including Pap [18], Ralescu and Adams [19] and, Wang and Klir [25], among others. RománFlores et al [9, 20–23], started the studies of inequalities for Sugeno integral, and the...

In this article, we obtain generalizations for Grüss type integral inequality by using h(x)-Riemann-Liouville fractional integral.

In this paper, using the Riemann-Liouville fractional q-integral, we establish some new fractional integral inequalities by using two parameters of deformation q1 and q2.

By Hölder's integral inequality, the authors establish some Hermite-Hadamard type integral inequalities for n-times differentiable and geometrically quasi-convex functions.

In this paper, some Hermite-Hadamard-Fejer type integral inequalities for harmonically s-convex functions in fractional integral forms have been obtained.

A novel stability analysis for the interval time-delay systems is proposed by employing a new series of integral inequalities for single and double integrals. Different from the recently introduced Wirtinger-based inequalities, refined Jensen inequalities and auxiliary function-based inequalities, the proposed ones can provide more accurate bounds for the cross terms in derivatives of the Lyapu...