Related papers: A new generalization of Ostrowski type inequality …

This article used Bloch function to derive Schottky inequality, obtained its generalization by using elliptic integral deviation function and demonstrated its applications.

In this work, we obtain some new generalized weighted trapezoid and Gr\"uss type inequalities on time scales for parameter functions. Our results give a broader generalization of the results due to Pachpatte in \cite{Pach}. In addition, the…

In this paper, we give some {\L}ojasiewicz-type inequalities and a nonsmooth slope inequality on non-compact domains for continuous definable functions in an o-minimal structure. We also give a necessary and sufficicent condition for which…

We investigate several possibilities of obtaining a {\L}ojasiewicz inequality for definable multifunctions and give some examples of applications thereof. In particular, we prove that the Hausdorff distance and its extension to closed sets…

In this paper, new versions of Chebyshev's, Minkowski's and Holder's type inequalities are studied by using a monotone measure-base universal integral on an arbitrary measurable space. This paper generalizes some previous results obtained…

First and second-order inequalities of Friedrichs type for Sobolev functions in arbitrary domains are offered. The relevant inequalities involve optimal norms and constants that are independent of the geometry of the domain. Parallel…

In this paper, we establish some new general Opial inequalities for Widder derivatives.

In this paper we prove a sharp Ostrowski type inequality for random processes of certain classes. This inequality is later applied to a solution of the optimal recovery of the integral $\int_0^1\xi_tdt$, using the random variables…

We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta…

A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…

Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.

We derive inequalities for sums of eigenvalues of Schr\"{o}dinger operators on finite intervals and tori. In the first of these cases, the inequalities converge to the classical trace formulae in the limit as the number of eigenvalues…

In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.

In this paper, we establish some integral ineuqalities for n- times differentiable convex functions.

In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…

We investigate the fractional Orlicz boundary Hardy-type inequality for bounded Lipschitz domains. Further, we establish fractional Orlicz boundary Hardy-type inequalities with logarithmic corrections for specific critical cases across…

In this work, a generalization of Chebyshev functional is presented. New inequalities of Gruss type via Pompeiu's mean value theorem are established. Improvements of some old inequalities are proved. A generalization of pre-Gruss inequality…

In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the $\psi$-Hilfer fractional derivative…

We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some…

Famous Redheffer's inequality is generalized to a class of anti-periodic functions. We apply the novel inequality to the generalized trigonometric functions and establish several Redheffer-type inequalities for these functions.