In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a conventional differential inequality studied in the literature, but also handles non-differentiable or disco...

In this paper, to concern the delay-dependent stability criterion, we adopt the integral inequality lemma on the LR method. Some variables are introduced to relax the integral term that is generated by the integral inequality lemma. Actually, the form of the criterion shows that, without any model transformations, we can obtain a stability criterion that can be extended to the stabilization pro...

The integral inequalities occupy privileged position in the theory of differential and integral equations. In the recent years nonlinear integral inequalities have received considerable attention because of their important applications to a variety of problems in diverse fields of nonlinear differential and integral equations. In 1919, Gronwall [4] introduced the famous Gronwall inequality in t...

An inequality for a companion of Ostrowski's integral inequality is proved. Application to a composite quadrature rule is considered.

minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. also related inequalities to minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. several examples are given to illustrate the validity of theorems. some results on chebyshev and minkowski type inequalities are obtained.

In this paper it is shown that a new Hardy-Hilbert type integral inequality can be established by introducing a proper integral kernel function, and that the constant factor is proved to be the best possible. In particular, for case p = 2, a new Hilbert type integral inequality is given .And as the mathematics aesthetics, several important constants π and Euler number En appear simultaneously i...

In this paper, we  present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given.

In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality depended on another function. This conditions is analogous of Banach conditions and general contraction condition of integral type.

This paper deals with a relation between Hardy-Hilbert’s integral inequality and Mulholland’s integral inequality with a best constant factor, by using the Beta function and introducing a parameter λ. As applications, the reverse, the equivalent form and some particular results are considered.