Bounding the Čebyšev Functional for the Riemann-Stieltjes Integral via a Beesack Inequality and Applications

Lower and upper bounds of the Čebyšev functional for the Riemann- Stieltjes integral are given. Applications for the three point quadrature rules of functions that are n-time differentiable are also provided

Approximating the Riemann-Stieltjes Integral via Some Moments of the Integrand

Error bounds in approximating the Riemann-Stieltjes integral in terms of some moments of the integrand are given. Applications for p-convex functions and in approximating the Finite Foureir Transform are pointed out as well

Some Remarks on the Trapezoid Rule In Numerical Integration

In this paper, by the use of some classical results from the Theory of Inequalities, we point out quasi-trapezoid quadrature formulae for which the error of approximation is smaller than in the classical case. Examples are given to demonstrate that the bounds obtained within this paper may be tighter than the classical ones. Some applications for special means are also given

Refinements of Some Reverses of Schwarz's Inequality in 2-Inner Product Spaces and Applications for Integrals

Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided

Some Inequalities for the Dispersion of a Random Variable whose PDF is Defined on a Finite Interval

Some inequalities for the dispersion of a random variable whose pdf is defined on a finite interval and applications are given

Norm Estimates for the Difference Between Bochner's Integral and the Convex Combination of Function's Values

Norm estimates are developed between the Bochner integral of a vector-valued function in Banach spaces having the Radon-Nikodym property and the convex combination of function values taken on a division of the interval [a,b]

Approximation of the Stieltjes integral and applications in numerical integration

summary:Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications to the Fourier Sine and Cosine transforms on finite intervals are mentioned as well

On inequalities of Jensen-Ostrowski type

We provide new inequalities of Jensen-Ostrowski type, by considering bounds for the magnitude of (Formula Presented), with various assumptions on the absolutely continuous function f:[a,b]→C and a μ-measurable function g, and a complex number λ. Inequalities of Ostrowski and Jensen type are obtained as special cases, by setting λ=0 and ζ=∫Ωgdμ, respectively. In particular, we obtain some bounds for the discrepancy in Jensen’s integral inequality. Applications of these inequalities for f-divergence measures are also given