Ismail Nikoufar, Davuod Saeedi
In this paper, we provide some inequalities for $P$-class functions and self-adjoint operators on a Hilbert space including an operator version of the Jensen's inequality and the Hermite-Hadamard's type inequality. We improve the Hölder-MacCarthy inequality by providing an upper bound. Some refinements of the Jensen type inequality for $P$-class functions will be of interest.
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In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of Gressman [8]. In particular, we establish optimisers for these determinant inequalities. We then use these inequalities to establish our main theorem which gives a geometric inequality of matrix type which improves and extends some inequalities of Christ in [5].
We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.
We prove a trace Hardy type inequality with the best constant on the polyhedral convex cones which generalizes recent results of Alvino et al. and of Tzirakis on the upper half space. We also prove some trace Hardy-Sobolev-Maz'ya type inequalities which generalize the recent results of Filippas et al.. In applications, we derive some Hardy type inequalities and Hardy-Sobolev-Maz'ya type inequalities for fractional Laplacian. Finally, we prove the logarithmic Sobolev trace inequalities and logarithmic Hardy trace inequalities on the upper half spaces. The best constants in these inequalities ar…
In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite- Hadamard integral inequality for mappings whose derivatives are (h -($α$?;m))-convex.The generalized integral inequalities contribute some better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.
We introduce some symmetric homogeneous means, and then show unitarily invariant norm inequalities for them, applying the method established by Hiai and Kosaki. Our new inequalities give the tighter bounds of the logarithmic mean than the inequalities given by Hiai and Kosaki. Some properties and norm continuities in parameter for our means are also discussed.
We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian matrix.
In this paper, we introduce the concept of operator arithmetic-geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities for operators which give some refinements of previous results. Moreover, some unitarily invariant norm inequalities are established.
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.
This research aimed to explore some new Hermite-Hadamard inequalities for strongly harmonic convex set-valued functions with modulus c > 0 introduced by G. Santana
The purpose of this paper is two-fold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to generalize and improve the Hua-Marcus' inequalities. Our results are stronger and more general than the existing ones.
This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are also included.
In this paper, we present a simple proof of a recent result of the second author which establishes that functional inverse-Santal{ó} inequalities follow from Entropy-Transport inequalities. Then, using transport arguments together with elementary correlation inequalities, we prove these sharp Entropy-Transport inequalities in dimension 1. We also revisit the proof of the functional inverse-Santal{ó} inequalities in the n dimensional unconditional case using these ideas.
In this paper we prove the Fractional Gagliardo-Nirenberg Inequality, Polya-Szego Inequality and the Sharp Fractional Sobolev Inequality, we then provide an application of such inequalities in a constraiend variational problem involving the fractional gradient and alocal non-linearity
The goal of the present paper is to discuss new transport inequalities for convex measures. We retrieve some dimensional forms of Brascamp-Lieb inequalities. We also give some quantitative forms involving the Wasserstein's distances.
In this paper, new versions of Chebyshev's, Minkowski's and Holder's type inequalities are studied by using a monotone measure-base universal integral on an arbitrary measurable space. This paper generalizes some previous results obtained by many researchers.
In this paper we obtain some operator versions of Levin-Steckin integral inequality.
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.
In this paper we show different inequalities for fractional order differential operators. In particular, the Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for the Caputo, Riemann-Liouville and Hadamard derivatives are obtained. In addition, we show some applications of these inequalities.
Some reverse inequalities for scalar Birkhoff weak integrable functions
本文研究了标量Birkhoff弱可积函数在非加法测度下的Hölder和Minkowski不等式及其反向不等式。
In this paper, we obtained some inequalities for ϕ_{s}-convex function, ϕ-Godunova-Levin function, ϕ-P-function and log-ϕ-convex function. Finally, we defined the class of ϕ-quasi-convex functions and we examined some properties of this class.
In this paper we establish some companions of perturbed Ostrowski type integral inequalities for functions whose second derivatives are bounded. Some applications to composite quadrature rules, and to probability density functions are also given.
K-frame theory was recently introduced to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space. This significant property is worthwhile especially in some problems arising in sampling theory. Some equalities and inequalities have been established for ordinary frames and their duals. In this paper, we continue and extend these results to obtain several important equalities and inequalities for K-frames. Moreover, by applying Jensen's operator inequality we obtain some new inequalities for $K$-frames.
In this paper, some Ostrowski type inequalities via Riemann-Liouville fractional integrals for h-convex functions, which are super-multiplicative or super-additive, are given. These results not only generalize those of Set (2012) and Tunc (2012), but also provide new estimates on these types of Ostrowski inequalities for fractional integrals.
We give some new refinements of Heinz inequality and an improvement of the reverse Young's inequality for scalars and we use them to establish new inequalities for operators and the Hilbert-Schmidt norm of matrices. We give a uniformly and abbreviated form of the inequalities presented by Kittaneh and Mansarah, and the inequalities presented by Kai and we obtain some of their operator and matrix versions.
In this paper we first introduce the Heron and Heinz means of two convex functionals. Afterwards, some inequalities involving these functional means are investigated. The operator versions of our theoretical functional results are immediately deduced. We also obtain new refinements of some known operator inequalities via our functional approach in a fast and nice way.
In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.
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 integral inequalities via Caputo and Liouville fractional integral operators for m-convex functions
本文利用基本不等式和m-凸函数性质，获得了包含Caputo分数阶导数的新积分不等式，并给出了文献引理左边的上界。
In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.
We will consider about some inequalities on operator means for more than three operators, for instance, ALM and BMP geometric means will be considered. Moreover, log-Euclidean and logarithmic means for several operators will be treated.
In this short note, we first consider some inequalities for comparison of some algebraic properties of two continuous algebra-multiplications on an arbitrary Banach space and then, as an application, we consider some very basic observations on the space of all continuous algebra-multiplications on a Banach space.
The weighted numerical radius of a Hilbert space operator has been defined recently. This article explores other properties and uses this newly defined numerical radius to obtain several new interesting inequalities for the weighted numerical radius and the numerical radius. In particular, new identities for the numerical radius, further comparisons between the numerical radius and the real and imaginary parts, and some inequalities for sectorial operators will be presented.
In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite-Hadamard integral inequality for mappings whose derivatives are $s$-$(α,m)$-convex.The generalised integral inequalities contribute some better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.
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.
Continuous generalized fusion frame theory was recently introduced by Rahimi and al. Several equalities and inequalities have been obtained for frame, fusion generalized fusion frame, among others. In the present paper, we continue and extend these results to obtain some important identities and inequalities in the case of continuous generalized fusion frame, Parceval continuous generalized fusion frame, $ λ$-tight continuous generalized fusion frame. Moreover, we obtain some new inequalities for the alternate dual continuous generalized fusion frame. Finally, we obtain frame operator of a pai…
In this paper, we establish some new Hadamard type inequalities using elementary well known inequalities for functions whose inequalities absolute values are α-, m-, (α,m)-logarithmically convex.
Some inequalities of Cauchy-Bunyakovsky-Schwarz type for sequences of bounded linear operators in Hilbert spaces and some applications are given.
In this paper, we obtain some new inequalities for functions which are introduced by Godunova and Levin.
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
In this paper we obtain some weighted generalizations of Ostrowski type inequalities on time scales involving combination of weighted Δ-integral means, i.e., a weighted Ostrowski type inequality on time scales involving combination of weighted Δ-integral means, two weighted Ostrowski type inequalities for two functions on time scales, and some weighted perturbed Ostrowski type inequalities on time scales. We also give some other interesting inequalities and recapture some known results as special cases.
In this paper we establish some new Hermite-Hadamard type inequalities for two operator convex functions of selfadjoint operators in Hilbert spaces.
In this paper we establish some new inequalities of Hadamard-type for product of convex and s-convex functions in the second sense.
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.
Some new counterparts of Bessel's inequality for orthornormal families in real or complex inner product spaces are pointed out. Applications for some Gruss type inequalities are also empahsized.
We study in this article some Sobolev-type inequalities on polynomial volume growth Lie groups. We show in particular that improved Sobolev inequalities can be extended without the use of the Littlewood-Paley decomposition to this general framework.
This article is devoted to studying some new numerical radius inequalities for Hilbert space operators. Our analysis enables us to improve an earlier bound of numerical radius due to Kittaneh.
In this paper, a general form of integral inequalities of Hermite-Hadamard's type through differentiability for s-Convex function in second sense and whose all derivatives are absolutely continuous are established. The generalized integral inequalities contributes some better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.
Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
Some inequalities for log-convex functions of selfadjoint operators on quaternionic Hilbert spaces
本文针对四元数希尔伯特空间上的自伴算子，利用对数凸函数证明了若干Jensen型不等式，并通过特定对数凸函数得到算子不等式的特殊情况，丰富了该领域的不等式研究。
Using some harmonic extensions on the upper-half plane, and probabilistic representations, and curvature-dimension inequalities with some negative dimensions, we obtain some new opimal functional inequalities of the Beckner type for the Cauchy type distributions on the Euclidean space. These optimal inequalities appear to be equivalent to some non tight optimal Beckner inequalities on the sphere, and the family appear to be a new form of the Sobolev inequality.
Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type inequalities. The matrix approach may also provide simplified proofs and new results for classical inequalities. For instance, we show a link between Cassel's inequality and the basic rearrangement inequality for sequences of Hardy-Littlewood-Polya, and we state a reverse inequality to the Hardy-Littlewood-Polya inequality in which matrix technics are essential.
In this paper, we establish some new Hadamard type inequalities for s-logarithmically convex functions in the second sense via fractional integrals by using Lemma 1 which has been proved by Sarikaya et al. in the paper [3].
We observe some higher order Poincare-type inequalities on a closed manifold, which is inspired by Hurwitz's proof of the Wirtinger's inequality using Fourier theory. We then give some geometric implication of these inequalities by applying them on the sphere. More specifically, by applying them to the support function of a convex hypersurface in the Euclidean space, we obtain some sharp Minkowski-type inequalities, such as a stability inequality for the classical Minkowski inequality and the Alexandrov-Fenchel inequality.
In this paper, we describe s-logarithmically convex functions in the first and second sense which are connected with the ordinary logatihmic convex and s-convex in the first and second sense. Afterwards, some new inequalities related to above new definitions are given.
In this work, we investigate the tensor inequalities in the tensor t-product formalism. The inequalities involving tensor power are proved to hold similarly as standard matrix scenarios. We then focus on the tensor norm inequalities. The well-known arithmetic-geometric mean inequality, H{\" o}lder inequality, and Minkowski inequality are generalized to tensors. Furthermore, we obtain some t-eigenvalue inequalities.
We determine the optimal orders for the best constants in the non-commutative Burkholder-Gundy, Doob and Stein inequalities obtained recently in the non-commutative martingale theory.
We discuss transportation cost inequalities for uniform measures on convex bodies, and connections with other geometric and functional inequalities. In particular, we show how transportation inequalities can be applied to the slicing problem, and give a new log-Sobolev-type inequality for bounded domains in R^n.
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