Related papers: On some extremalities in the approximate integrati…
We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, the convergence has already been…
We provide sufficient conditions for quantitative convergence of the iterates of proximal splitting algorithms for minimizing a sum of functions on a metric space. The theory does not assume that the functions have common minima, nor does…
We have recently established some integral inequalities for convex functions via the Hermite-Hadamard's inequalities. In continuation here, we also establish some interesting new integral inequalities for convex functions via the…
This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
We obtain estimates in simultaneous approximation for a summation-integral type genuine hybrid operator. The convergence of derivatives of operator to the corresponding derivatives of the functions is proved and estimates for rate of…
Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework…
An optimal 3-point quadrature formula of closed type is derived. Various error inequalities are established. Applications in numerical integration are also given.
The main target of this paper is to discuss operator Hermite--Hadamard inequality for convex functions, without appealing to operator convexity. Several forms of this inequality will be presented and some applications including norm and…
We consider M-estimators and derive supremal-inequalities of exponential-or polynomial type according as a boundedness- or a moment-condition is fulfilled. This enables us to derive rates of r-complete convergence and also to show r-qick…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
In this paper, approximate lower and upper Hermite--Hadamard type inequalities are obtained for functions that are approximately convex with respect to a given Chebyshev system.
We present a family of high order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of…
In this paper, firstly we have established Hermite-Hadamard's inequalities for s-convex functions in the second sense and m-convex functions via fractional integrals. Secondly, a Hadamard type integral inequality for the fractional…
In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
In this paper, new integral inequalities of Hadamard type involving several differentiable \Phi-r-convex functions are given.
A method of deriving quadrature rules has been developed which gives nodes and weights for a Gaussian-type rule which integrates functions of the form: f(x,y,t) = a(x,y,t)/((x-t)^2+y^2) + b(x,y,t)/([(x-t)^2+y^2]^{1/2}) +…
A generalization of classical determinant inequalities like Hadamard's inequality and Fischer's inequality is studied. For a version of the inequalities originally proved by Arveson for positive operators in von Neumann algebras with a…
In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of…
In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.