11,571 research outputs found
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
New Inequalities of Steffensen's type for s-convex functions
In this work, new inequalities connected with the Steffensen's integral
inequality for s-convex functions are provedComment: 8 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 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
Some properties of h-MN-convexity and Jensen's type inequalities
In this work, we introduce the class of --convex functions by
generalizing the concept of -convexity and combining it with
-convexity. Namely, Let be two intervals subset of
such that and
. Consider a non-negative function and let be a Mean function given by
; where
by we mean one of the following
functions: ,
and ; with the property that
and .
A function is said to be
--convex (concave) if the inequality \begin{align*} f
\left({\rm{M}}\left(t;x, y\right)\right) \le (\ge) \, {\rm{N}}\left(h(t);f (x),
f (y)\right), \end{align*} holds for all and , where M
and N are two mean functions. In this way, nine classes of
--convex functions are established and some of their analytic
properties are explored and investigated. Characterizations of each type are
given. Various Jensen's type inequalities and their converses are proved.Comment: 27 pages. Journal of Interdisciplinary Mathematics 201
On the generalized mixed Schwarz inequality
In this work, an extension of the generalized mixed Schwarz inequality is
proved. A companion of the generalized mixed Schwarz inequality is established
by merging both Cartesian and Polar decompositions of operators. Based on that
some numerical radius inequalities are proved.Comment: 14 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
Bounds for the difference between two \v{C}eby\v{s}ev functionals
In this work, a generalization of pre-Gr\"{u}ss inequality is established.
Several bounds for the difference between two \v{C}eby\v{s}ev functional are
proved.Comment: 18 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
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