164,794 research outputs found
A General Ostrowski Type Inequality for Double Integrals
No full textSome generalisations of an Ostrowski Type Inequality in two dimensions for n-time differentiable mappings are given. The result is an Integral Inequality with bounded n-time derivatives. This is employed to approximate double integrals using one dimensional integrals and function evaluations at the boundary and interior points
Ostrowski Type Inequality for Absolutely Continuous Functions on Segments in Linear Spaces
No full textAn Ostrowski type inequality is developed for estimating the
deviation of the integral mean of an absolutely continuous function, and
the linear combination of its values at k + 1 partition points, on a segment
of (real) linear spaces. Several particular cases are provided which
recapture some earlier results, along with the results for trapezoidal type
inequalities and the classical Ostrowski inequality. Some inequalities are
obtained by applying these results for semi-inner products; and some of
these inequalities are proven to be sharp
Sharp Inequalities of Ostrowski Type for Convex Functions Defined on Linear Spaces and Application
No full textAn Ostrowski type inequality for convex functions defined on linear spaces is generalised.
Some inequalities which improve the Hermite–Hadamard type inequality for convex
functions defined on linear spaces are derived using the obtained result. The results in
normed linear spaces are used to obtain some inequalities which are related to the given
norm and associated semi-inner products, and to prove the sharpness of the constants in
those inequalities
Two Ostrowski Type Inequalities for the Stieltjes Integral of Monotonic Functions
No full textTwo integral inequalities of Ostrowski type for the Stieltjes integral
are given. The first is for monotonic integrators and Holder continuous
integrands while the second considers the dual case, i.e., for monotonic integrands
and Holder continuous integrators. Applications for the mid-point
inequality that are useful in the numerical analysis of Stieltjes integrals are
exhibited. Some connections with the generalised trapezoidal rule are also
presented
On Ostrowski Type Inequalities for Stieltjes Integrals with Absolutely Continuous Integrands and Integrators of Bounded Variation
No full textSome Ostrowski type inequalities are given for the Stieltjes integral
where the integrand is absolutely continuous while the integrator is of
bounded variation. The case when |f'| is convex is explored. Applications for
the midpoint rule and a generalised trapezoid type rule are also presented
Chebychev Functional Bounds Using Ostrowski Seminorms
No full textBounds are obtained for the Chebychev functional using what is termed as the Ostrowski seminorm which is related to an inequality developed by Ostrowski. The Ostrowski seminorm is also compared to the △−seminorm introduced in earlier work by the authors
The Unified Treatment of Trapezoid, Simpson and Ostrowski Type Inequality for Monotonic Mappings and Applications
No full textWe give new trapezoid inequality as well as Simpson and Ostrowski type inequalities for monotonic functions. We provide their applications in Probability Theory, Numerical Analysis and for Special Means
Improvement of an Ostrowski Type Inequality for Monotonic Mappings and its Application for Some Special Means
No full textWe first improve two Ostrowski type inequalities for monotonic functions, then provide its application for special means
A Generalization of Ostrowski Integral Inequality for Mappings Whose Derivatives Belong to L₁ [a,b] and Applications in Numerical Integration
No full textA generalization of Ostrowski integral inequality for mappings whose derivatives belong to L₁[a,b], and applications for general quadrature formulae are given
An Inequality of the Ostrowski Type For Double Integrals and Applications for Cubature Formulae
No full textWe point out a new inequality of the Ostrowski type for mappings of two independent variables, which complements, in a sense, some recent results and apply it to the approximation problem of double integrals by their Riemann sums
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