arXiv subjects
Publications and source records attributed to Silvestru Sever Dragomir.
Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.
In this paper we obtain some operator versions of Levin-Steckin integral inequality.
In this paper, obtained some new class of Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities via fractional integrals for the p-hyperbolic convex functions. It is shown that such inequalities are simple consequences of Hermite-Hadamard-Fejer inequality for the p-hyperbolic convex function.
We present several operator extensions of the Chebyshev inequality for Hilbert space operators. The main version deals with the synchronous Hadamard property for Hilbert space operators. Among other inequalities, it is shown that if ${\mathfrak A}$ is a $C^*$-algebra, $T$ is a compact Hausdorff space equipped with a Radon measure $μ$ as a totaly order set, then \begin{align*} \int_{T} α(s) dμ(s)\int_{T}α(t)(A_t\circ B_t) dμ(t)\geq\Big{(}\int_{T}α(t) (A_tm_{r,α} B_t) dμ(t)\Big{)}\circ\Big{(}\int_{T}α(s) (A_sm_{r,1-α} B_s) dμ(s)\Big{)}, \end{align*} where $α\in[0,1]$, $r\in[-1,1]$ and $(A_t)_{t\in T}, (B_t)_{t\in T} $ are positive increasing fields in $\mathcal{C}(T,\mathfrak A)$.
In this paper we introduce the hypo-q-norms on a Cartesian product of normed linear spaces. A representation of these norms in terms of bounded linear functionals of norm less than one, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar Shisha-Mond, Birnacki et al. and other Gruss type inequalities are also given.
Some improvements of the celebrated Schwarz inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided.
We establish in this paper some inequalities for analytic and convex functions on an open interval and positive normalized functionals defined on a Hermitian unital Banach *-algebra. Reverses and refinements of Jensen's and Slater's type inequalities are provided. Some examples for particular convex functions of interest are given as well.
In this paper we introduce the quadratic weighted geometric mean for invertible elements x, y in a Hermitian unital Banach star-algebra and provide some inequalities for this mean under various assumptions for the elements involved.
In this paper we introduce the concept of quadratic operator perspective for a continuous function Φ defined on the positive semi-axis of real numbers. This generalize the quadratic weighted operator geometric mean and the quadratic relative operator entropy. Some inequalities for this perspective of convex functions are established. Applications for quadratic weighted operator geometric mean and quadratic relative operator entropy are also provided.
In this paper, we give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point.
In this paper we obtain some new refinements and reverses of Young's operator inequality. Extensions for convex functions of operators are also provided.
Some inequalities for quantum f-divergence of trace class operators in Hilbert spaces are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and chi-distance are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.
By the use of the celebrated Kato's inequality we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space H. Natural applications for functions defined by power series of normal operators are given as well.
Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace inequalities for matrices are also derived. Examples for the operator exponential and other similar functions are presented as well.
The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The inequalities obtained here have direct applications in Numerical Integration, Probability Theory, Information Theory and Integral Operator Theory. Some of these applications are discussed.
The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone .The current article obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. A variety of earlier results are recaptured as particular instances of the current development. Applications for cumulative distribution function are also discussed.
The main aim of this book is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.