Related papers: Generalized retarded integral inequalities
We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…
The following class of retarded integro-differential equations in a Banach space \[ \dot{x}\left(t\right)=Ax\left(t\right)+\int_{0}^{t}b\left(t-\tau\right)Lx_{\tau}d\tau+Kx_{t};\,\,t\geq0, \] are taken into consideration in this study. The…
Certain new inequalities for the sums of factorials are presented.
The paper discusses the summability of formal solutions of some linear q-difference-differential equations, and improves the previous result in [Tahara-Yamazawa, Opsucula Math. 35 (2015), 713-738].
Some new Hermite-Hadamard's inequalities for h-convex functions are proved, generalizing and unifying a number of known results. Some new applications for special Means of real numbers are also derived.
In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
The principal aim of this paper is to extend Birman's sequence of integral inequalities originally obtained in 1961, and containing Hardy's and Rellich's inequality as special cases, to a sequence of inequalities that incorporates power…
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968
In this paper, we study the further improvements of the reverse Young and Heinz inequalities for the wider range of $v$, namely $v\in \mathbb{R}$. These modified inequalities are used to establish corresponding operator inequalities on a…
In this note, we present an information diffusion inequality derived from an elementary argument, which gives rise to a very general Fano-type inequality. The latter unifies and generalizes the distance-based Fano inequality and the…
In the paper, two new identities involving the local fractional integrals have been established. Using these two identities, we obtain some generalized Hermite-Hadamard type integral inequalities for the local differentiable generalized…
We prove that characteristic equations of certain types of delay differential systems, under some mild conditions on their coefficients, can possess infinitely many complex roots.
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised $\sin_{p,q}$ in two parameters. A striking generalisation of the improper Dirichlet integral is achieved. A second surprising…
In the paper, the authors review several refinements of Young's integral inequality via several mean value theorems, such as Lagrange's and Taylor's mean value theorems of Lagrange's and Cauchy's type remainders, and via several fundamental…
A review of the properties of this alternate basis is presented. To appear in the proceedings of the 3rd Workshop on Thermal Field Theory, Banff, August 1993.
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.