304 research outputs found
New sharp inequalities of Ostrowski and generalized trapezoid type for the Riemann-Stieltjes integrals and applications
In this paper, new sharp weighted generalizations of Ostrowski and
generalized trapezoid type inequalities for the Riemann--Stieltjes integrals
are proved. Several related inequalities are deduced and investigated. New
Simpson's type inequalities for --integral are pointed out.
Finally, as application; an error estimation of a general quadrature rule for
--integral via Ostrowski--generalized trapezoid quadrature
formula is given.Comment: 22 page
q-Bernoulli Inequality
In this work, the q-analogue of Bernoulli inequality is proved. Some other
related results are presented.Comment: 7 page
The Hermite-Hadamard inequality on hypercuboid
Given any and
in . The
-fold convex function defined on , with is a
convex function in each variable separately. In this work we prove an
inequality of Hermite-Hadamard type for -fold convex functions.
Namely, we establish the inequality \begin{align*} f\left( {\frac{{{\bf{a}} +
{\bf{b}}}}{2}} \right) \le \frac{1}{{{\bf{b}} -
{\bf{a}}}}\int_{\bf{a}}^{\bf{b}} {f\left( {\bf{x}} \right)d{\bf{x}}} \le
\frac{1}{{2^n }}\sum\limits_{\bf{c}} {f\left( {\bf{c}} \right)}, \end{align*}
where . Some other related result are given.Comment: 12 page
Pompeiu-Chebyshev type inequalities for selfadjoint operators in Hilbert spaces
In this work, generalization of some inequalities for continuous
-synchronous (-asynchronous) functions of selfadjoint linear operators in
Hilbert spaces are proved.Comment: 14 page
On Pompeiu-Chebyshev functional and its generalization
In this work, a generalization of Chebyshev functional is presented. New
inequalities of Gruss type via Pompeiu's mean value theorem are established.
Improvements of some old inequalities are proved. A generalization of pre-Gruss
inequality is elaborated. Some remarks to further generalization of Chebyshev
functional are presented. As applications, bounds for the reverse of CBS
inequality are deduced. Hardy type inequalities on bounded real interval [a,b]
under some other circumstances are introduced. Other related ramified
inequalities for differentiable functions are also given.Comment: 30 page
An Inequality of Simpson's type Via Quasi-Convex Mappings with Applications
In this paper, an inequality of Simpson type for quasi-convex mappings are
proved. The constant in the classical Simpson's inequality is improved.
Furthermore, the obtained bounds can be (much) better than some recently
obtained bounds. Application to Simpson's quadrature rule is also given.Comment: 7 pages, no figur
Popoviciu's type inequalityies for h-MN-convex functions
In this work, several inequalities of Popoviciu type for h-MN-convex
functions are proved, where M or N are denote to Arithmetic, Geometric and
Harmonic means and is a non-negative superadditive or subadditive function.Comment: 26 page
On Alzer's inequality
Extensions and generalizations of Alzer's inequality; which is of Wirtinger
type are proved. As applications, sharp trapezoid type inequality and sharp
bound for the geometric mean are deduced.Comment: 8 page
Operator Popoviciu's inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces
In this work, operator version of Popoviciu's inequality for positive
selfadjoint operators in Hilbert spaces under positive linear maps for
superquadratic functions is proved. Analogously, using the same technique
operator version of Popoviciu's inequality for convex functions is obtained.
Some other related inequalities are also deduced.Comment: 11 page
Refinements of Some Numerical radius inequalities for Hilbert Space Operators
In this work, some generalizations and refinements inequalities for numerical
radius of the product of Hilbert space operators are proved. New inequalities
for numerical radius of block matrices of Hilbert space operators are also
established.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1810.05710,
arXiv:1810.1006
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