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

The time dependent net maternity function

This thesis examines the resultant behaviour of a population in response to change of the age-specific birth and death rates with time. The deterministic one sex population model of Sharpe and Lotka is used as the basis for the analysis. In particular, the asymptotic behaviour is determined for a population with a time dependent net maternity function. Thus, the present study may be looked upon as representing a generaliisation of the stble population theory to include models of time dependent vital rates of birth and death. Lplace transform techniques are used extensively throughout the present work

ON ZETA AND DIRICHLET BETA FUNCTION FAMILIES AS GENERATORS OF GENERALIZED MATHIEU SERIES, PROVIDING APPROXIMATION AND BOUNDS

Integral representations for a generalized Mathieu series and its companions are used to undertake analysis leading to novel insights for Zeta and Dirichlet Beta function families. The bounds are procured using sharp bounds of Zeta and Dirichlet family bounds to procure approximating and bounds utilising integral representation of generalized Mathieu series results using in particular Hardy-type upper bounds

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

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

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

Comparing Two Integral Means for Absolutely Continuous Mappings Whose Derivatives are in L∞[a,b] and Applications

Estimates of the difference of two integral means on [a,b], [c,d] with [c,d] ⊂ [a,b] in terms of the sup norm of the derivative and applications for pdfs, special means, Jeffreys’ divergence and continuous streams are given