Young Type Inequalities Research Articles

On some extensions of the Hua determinant inequality and a question of Poon

In this note, we give simple proofs of two recent extensions of the Hua determinant inequality. We also answer a question of Poon affirmatively on a Young type inequality, which appears in his investigation of inequalities on eigenvalues arising from the Hua determinant inequality.

Enhanced Young-type inequalities utilizing Kantorovich approach for semidefinite matrices

Abstract This article introduces new Young-type inequalities, leveraging the Kantorovich constant, by refining the original inequality. In addition, we present a range of norm-based inequalities applicable to positive semidefinite matrices, such as the Hilbert-Schmidt norm and the trace norm. The importance of these results lies in their dual significance: they hold inherent value on their own, and they also extend and build upon numerous established results within the existing literature.

Some new Young type inequalities

<abstract><p>In this paper, we gave some generalized Young type inequalities due to Zuo and Li [J. Math. Inequal., 16 (2022), 1169-1178], and we also presented a new Young type inequality. As applications, we obtained some operator inequalities and matrix versions inequalities including the Hilbert-Schmidt norm and trace.</p></abstract>

Some refinements of Young type inequalities

Some refinements of Young type inequalities

On the generalized Fourier transform

In this paper, we introduce the theory of a generalized Fourier transform in order to solve differential equations with a generalized fractional derivative, and we state its main properties. In particular, we obtain the new corresponding convolution, inverse and Plancherel formulas, and Hausdorff–Young type inequality. We show that this generalized Fourier transform is useful in the study of several fractional differential equations (both ordinary and partial differential equations).

Young inequalities for a Fourier cosine and sine polyconvolution and a generalized convolution

In this paper, we obtain some Young type inequalities for a polyconvolution and a generalized convolution involving the Fourier-cosine and Fourier-sine integral transforms.

New versions of refinements and reverses of Young-type inequalities with the Kantorovich constant

Abstract Recently, some Young-type inequalities have been promoted. The purpose of this article is to give further refinements and reverses to them with Kantorovich constants. Simultaneously, according to the scalar result, we have obtained some corresponding operator inequalities and matrix versions, including Hilbert-Schmidt norm, unitary invariant norm, and trace norm can be regarded as Scalar inequality.

Further new refinements and reverses of real power form for Young-type inequalities via famous constants and applications

Further new refinements and reverses of real power form for Young-type inequalities via famous constants and applications

Generalizations of young-type inequalities via quadratic interpolation

Generalizations of young-type inequalities via quadratic interpolation

Strengthenings of Young-type inequalities and the arithmetic geometric mean inequality

Abstract In this paper, we present some generalizations and further refinements of Young-type inequality due to Choi [Math. Inequal. Appl. 21 (2018), 99–106], which strengthen the results obtained by Ighachane et al. [Math. Inequal. Appl. 23 (2020), 1079–1085]. As applications of these scalars results, we can get some inequalities for determinants, trace and p-norms of τ-measurable operators.

Some generalizations of real power form for Young-type inequalities and their applications

In this paper we propose some generalizations of real power form for Young-type inequalities which are much better than the recent results developed by many researchers. Our approaching method, together with idea on linear interpolation of Choi et al. (2017) [3], allows us to build very strict improvements of real power form for Young-type inequalities. As applications, we give the operator versions and inequalities involving unitarily invariant norms and determinants of matrices.

A new generalization of Young type inequality and applications

In this paper, we give refinements of the classical Young inequality for scalars and we use these refinements to establish refined some Young type inequalities for the trace, determinants, and norms of positive definite matrices.

On the solution of a class of integral equations using new weighted convolutions

This paper is devoted to the study of the solvability of a class of integral equations, whose kernel depends on four different functions. To obtain necessary and sufficient conditions for the unique solution of this class of equations, we introduce eight new weighted convolutions associated with the kernel of our equations. Moreover, we obtain two Young-type inequalities associated with each convolution.

Some refinements of Young type inequalities

Some refinements of Young type inequalities

Some results of reverses young’s inequalities

In this paper, we present some refinements of reverse Young?s inequalities. Among other results, a refinement of reverse operator Young inequalities says A?vB + 2?(A?B ? A?B) ? m??M m??M / A?vB, where 0 < mI ? A, B ? MI, ? = min{v, 1 ? v} and v ? [0, 1], extending a key result in [J. Math. Anal. Appl. 465 (2018) 267-280] and [Linear Multilinear Algebra 67 (2019) 1567-1578]. Furthermore, we give a reverse of Young?s inequalities due to [Math. Slovaca 70 (2020), 453-466]. Moreover, we give a generalization of reverse Young-type inequality, and we also show a new Young-type inequality which is either better or not uniformly better than the main results in [Rocky Mountain J. Math. 46 (2016), 1089-1105]. As applications of these results, we obtain some inequalities for operators, Hilbert-Schmidt norms, unitarily invariant norms and determinants.

Convolutions and integral equations weighted by multi-dimensional Hermite functions

In this paper, we study the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are obtained. To achieve such a goal, the main technique consists in introducing eight new convolutions weighted by multi-dimensional Hermite functions and using them as convolutions somehow associated with our integral equations. In this way, two Young-type inequalities are also obtained.

Some refined Young type inequalities using different weights

The Young type inequality asserts that if [Formula: see text] are two positive real numbers, then for each [Formula: see text], we have [Formula: see text] In this paper, we obtain some new inequalities using two different weights. For example, if [Formula: see text], then [Formula: see text] [Formula: see text] where [Formula: see text] In addition, we refine some matrix inequalities for Unitarily invariant norms by applying the deduced numerical inequalities.

A new generalized refinements of Young’s inequality

In this paper, we show a new generalized refinement of Young's inequality. As applications we give some new generalized refinements of Young type inequalities for the traces, determinants, and norms of positive definite matrices.

On Young-type inequalities of measurable operators

Let be a semi-finite von Neumann algebra, be the set of all τ-measurable operators and be the generalized singular number of . We proved that if , and , then the Young-type inequality , for all t>0 holds.

Additive Refinements and Reverses of Young's Operator Inequality Via a Result of Cartwright and Field

In this paper we obtain some new additive refinements and reverses of Young's operator inequality via a result of Cartwright and Field. Comparison with other additive Young's type inequalities are also provided.