We aim to introduce a k-Struve function and investigate its various properties, including mainly certain inequalities associated with this function. One of the inequalities given here is pointed out to be related to the so-called classical Turán-type inequality. We also present a differential equation, several recurrence relations, and integral representations for this k-Struve function.

The local boundedness of weak solutions to variational inequalities (obstacle problem) with the linear growth condition is obtained. Consequently, an analogue of a theorem by Reshetnyak about a.e. differentiability of weak solutions to elliptic divergence type differential equations is proved for variational inequalities.

We survey the most used bounds for positive roots of polynomials and discuss their efficiency. We obtain new inequalities on roots of polynomials. Then we give new inequalities on roots of orthogonal polynomials, obtained from the differential equations satisfied by these polynomials. Mathematics subject classification (2000): 12D10, 68W30.

In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation inequalities. The conditions can be easily verified and implemented. We present two simulation examples to illust...

In this paper we present some new generalized retarded nonlinear integral inequalities of Gronwall-Bellman type. Using integral and differential skills, some new results which provide explicit bounds on unknown functions in integral inequalities are investigated. Some applications are also presented to illustrate the usefulness of some of our results.

Children's perceptions of social resource inequalities were investigated by measuring spontaneous explanations for race-based disparities in access to societal resources. Fifth graders (N = 139, M = 11.14 years, SD = .61 years) viewed animated vignettes depicting hypothetical resource inequalities between institutions serving children of African-American and European-American background. Childr...

By employing feedback control laws, the robust stochastic stability of distributed parameter large-scale control systems under random structural perturbations is investigated. The results are obtained by using vector Lyapunov-like functionals in the context of the block-comparison theorem, the theory of systems of differential inequalities, and decomposition-aggregation method. The complexity v...

In this paper, we study some new generalized 2D nonlinear Gronwall-Bellman type inequalities, which provide explicit bounds for unknown functions concerned, and are useful in the analysis of qualitative and quantitative properties for solutions to fractional differential and differential-integral equations. The presented inequalities are of new forms compared with the existing results so far in...

Shannon’s entropy power inequality characterizes the minimum differential entropy achievable by the sum of two independent random variables with fixed differential entropies. Since the pioneering work of Shannon, there has been a steady stream of results over the years, trying to understand the structure of Shannon’s entropy power inequality, as well as trying to develop similar entropy power i...

* Correspondence: sding@seattleu. edu Department of Mathematics, Seattle University, Seattle, WA 98122, USA Full list of author information is available at the end of the article Abstract In this paper, we prove both the local and global L -norm inequalities for Green’s operator applied to minimizers for functionals defined on differential forms in L -averaging domains. Our results are extensio...