1,721,249 research outputs found
Further Reverse Results for Jensen's Discrete Inequality and Applications in Information Theory
No full textSome new inequalities which counterpart Jensen’s discrete inequality and improve the recent results from S.S. DRAGOMIR, "A converse result for Jensen’s discrete inequality via Grüss’ inequality and applications in information theory" and S.S. DRAGOMIR, "A converse of the Jensen inequality for convex mappings of several variables and applications" are given. A related result for generalized means is established. Applications in Information Theory are also provided
Midpoint Type Rules from an Inequalities Point of View
No full textThe article investigates interior point rules which contain the midpoint as a special case, and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities. Thus the simplest open Newton-Cotes rules are examined. Both Riemann-Stieltjes and Riemann integrals are evaluated with a variety of assumptions about the integrand enabling the characterisation of the bound in terms of a variety of norms. Perturbed quadrature rules are obtained through the use of Grüss, Chebychev and Lupaş inequalities, producing a variety of tighter bounds. The implementation is demonstrated through the investigation of a variety of composite rules based on inequalities developed. The analysis allows the determination of the partition required that would assure that the accuracy the result would be within a prescribed error tolerance. It is demonstrated that the bounds of the approximations are equivalent to those obtained from a Peano kernel that produces Trapezoidal type rules
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
A New Upper Bound for the Kullback-Leibler Distance and Applications
No full textIn this paper we obtain another upper bound for the Kullback-Leibler distance than the bound obtained in [2] by N.M. Dragomir and S.S. Dragomir and point out that it can be better than the first one in certain cases
On Simpson's Inequality and Applications
No full textNew inequalities of Simpson type and their application to quadrature formulae in Numerical Analysis are given
Vector inequalities for powers of some operators in Hilbert spaces
No full textVector inequalities for powers of some operators in Hilbert spaces with applications
for operator norm, numerical radius, commutators and self-commutators
are given
Inequalities for Beta and Gamma Functions Via Some Classical and New Integral Inequalities
Full text linkIn this survey paper we present the natural application of certain integral inequalities such as, Chebychev's inequality for synchronous and asynchronous mappings, Holder's inequality and Gruss' and Ostrowski's inequalities for the celebrated Euler's Beta and Gamma functions. Natural applications dealing with some adaptive quadrature formulae which can be deduced from Ostrowski's inequality are also pointed out
Some Inequalities for Functions of Bounded Variation with Applications to Landau Type Results
No full textSome inequalities for functions of bounded variation that provide
reverses for the inequality between the integral mean and the p−norm for
p Є [1,∞] are established. Applications related to the celebrated Landau
inequality between the norms of the derivatives of a function are also pointed
out
A trapezoid type inequality for double integrals
No full textIn this paper, we point out a trapezoid like inequality for double integrals and apply it in connection with the Gruss inequality
Approximating the Stieltjes Integral via the Darst-Pollard Inequality
Full text linkAn approximation of the Stieltjes integral of bounded integrals
and continuous integrators via the Darst-Pollard inequality is given. Applications
for the generalised trapezoid formula and the Ostrowski inequality for
functions of bounded variation are also provided
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