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In this paper we obtain some new converses of the Holder and Minkowski inequalities for positive linear functionals. Our results also provide new converses in case of sums, integrals and time scales integrals. Further we obtain a converse of integral Minkowski's inequality on time scales. [ABSTRACT FROM AUTHOR]

We improve the generalized numerical radius version of the Heinz means inequalities by employing convexity and the Hermit-Hadamard inequality. Moreover, we present novel proofs for the generalized numerical radius of Heinz-type inequalities. [ABSTRACT FROM AUTHOR]

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.

This paper is devoted to study six novel inequalities associated with the Riesz‐type fractional integral operator for synchronous function and bounded function. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some improvements and generalizations of Young's inequalities on the arithmetic, geometric, and harmonic mean. For example, In addition, we obtain some new results for Young's inequality for operators. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce the notion of polyconvolution for Fourier‐cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms are investigated in detail. The Watson‐type theorem is given, to establish necessary and sufficient conditions for this operator to be isometric isomorphism (unitary) on L2(ℝ+)$$ {L}_2\left({\mathrm{\mathbb{R}}}_{+}\right) $$, and to get its inverse represented in the conjugate symmetric form. The correlation between the existence of polyconvolution with some weighted spaces is shown, and Young's type theorem, as well as the norm‐inequalities in weighted space, is also obtained. As applications, we investigate the solvability of a class of Toeplitz plus Hankel type integral equations and linear Barbashin's equations with the help of factorization identities of such polyconvolution. Several examples are provided to illustrate the obtained results to ensure their validity and applicability. [ABSTRACT FROM AUTHOR]

We formulate Hermite–Hadamard–Mercer type inequalities for ( A B K -FI) (Atangana–Baleanu Katagampula Fractional Integral) operators. We present new Dragomir–Agarwal type identities and establish a variants of Jensen–Hermite–Hadamard type inequalities involving A B K -FI operators for differentiable convex mappings. We present new bounds by employing Young and Hölder inequalities. We make links between our findings and a number of well-known discoveries in the literature. Finally, to support the effectiveness of our obtain results, we expose some inequalities examples in terms of Modified Bessel functions and matrices. The findings of this paper may lead to more research in this field. [ABSTRACT FROM AUTHOR]

We characterise the triples (p, q, r) for which the bi-linear λ -twisted convolution map B λ : (f , g) → f × λ g is bounded from L p (C n) × L q (C n) → L r (C n) for 1 ≤ p , q , r ≤ ∞ . This gives the analogue of Young’s inequality for the twisted convolution. [ABSTRACT FROM AUTHOR]

We study the p-Rényi entropy power inequality with a weight factor t on two independent continuous random variables X and Y. The extension essentially relies on a modulation on the sharp Young’s inequality due to Bobkov and Marsiglietti. Our research provides a key result that can be used as a fundamental research finding in quantum Shannon theory, as it offers a Rényi version of the entropy power inequality for quantum systems. [ABSTRACT FROM AUTHOR]

Fractional calculus has been a concept used to acquire new variants of some well-known integral inequalities. In this study, our primary goal is to develop majorized fractional Simpson's type estimates by employing a differentiable function. Practicing majorization theory, we formulate a new auxiliary identity by utilizing fractional integral operators. In order to obtain new bounds, we employ the idea of convex functions on the Niezgoda–Jensen–Mercer inequality for majorized tuples, along with some fundamental inequalities including the Hölder, power mean, and Young inequalities. Some applications to the quadrature rule and examples for special functions are provided as well. Interestingly, the main findings are the generalizations of many known results in the existing literature. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, for a function f: X → R, we introduce the following expression: Δλ (f)(x,y):=λ f (x)+(1-λ) f (y)- f (λ x+(1-λ)y), where x,y ∈X and λ ∈ R. The purpose of this article is to characterize this expression, by finding various estimates of it. We also give some characterizations of Δλ (f)(x,y) when function f is convex, which prove refinements of Young's inequality. Finally, we give several inequalities in a normed space. [ABSTRACT FROM AUTHOR]

This paper aims to present several new properties of geometrically convex functions similar to some those known properties for convex functions. Finally, we show some improvements of Young's inequality. [ABSTRACT FROM AUTHOR]

We investigate and prove a new lemma for twice differentiable functions with the fractional integral operator AB. Based on this newly developed lemma, we derive some new results about this identity. These new findings provide some generalizations of previous findings. This research builds on a novel new auxiliary result that allows us to create new variants of Ostrowski type inequalities for twice differentiable convex mappings. Some of the newly presented results' special cases are also discussed. As applications, several estimates involving special means of real numbers and Bessel functions are depicted.

Abstract In this article, the main objective is construction of fractional Newton–Simpson-type inequalities with the concept of majorization. We established a new identity on estimates of definite integrals utilizing majorization and this identity will lead us to develop new generalized forms of prior estimates. Some basic inequalities such as Hölder’s, power-mean, and Young’s along with the Niezgoda–Jensen–Mercer inequality have been used to obtain new bounds and it has been determined that the main findings are generalizations of many results that exist in the literature. Applications to the quadrature rule are given as well. We make links between our findings and a number of well-known discoveries in the literature.

In this article, we introduce the notion of $ _{a}{\bar{T}}_{p,q} $-integrals. Using the definition of $ _{a}{\bar{T}}_{p,q} $-integrals, we derive some new post quantum analogues of some classical results of Young's inequality, Hölder's inequality, Minkowski's inequality, Ostrowski's inequality and Hermite-Hadamard's inequality.

In this paper, we prove several new integral inequalities for the k-Hilfer fractional derivative operator, which is a fractional calculus operator. As a result, we have a whole new set of fractional integral inequalities. For the generalized fractional derivative, we also use Young's inequality to find new forms of inequalities. Such conclusions for this novel and generalized fractional derivative are extremely useful and valuable in the domains of differential equations and fractional differential calculus, both of which have a strong connections to real-world situations. These findings may stimulate additional research in a variety of fields of pure and applied sciences.

We investigate and prove a new lemma for twice differentiable functions with the fractional integral operator AB. Based on this newly developed lemma, we derive some new results about this identity. These new findings provide some generalizations of previous findings. This research builds on a novel new auxiliary result that allows us to create new variants of Ostrowski type inequalities for twice differentiable convex mappings. Some of the newly presented results' special cases are also discussed. As applications, several estimates involving special means of real numbers and Bessel functions are depicted. [ABSTRACT FROM AUTHOR]

Let μ be the Haar measure of a unimodular locally compact group G and m(G) as the infimum of the volumes of all open subgroups of G. The main result of this paper is that ∫ G f ∘ ϕ 1 ∗ ϕ 2 g d g ≤ ∫ R f ∘ ϕ 1 ∗ ∗ ϕ 2 ∗ x d x holds for any measurable functions ϕ 1 , ϕ 2 : G → R ≥ 0 with μ (supp ϕ 1) + μ (supp ϕ 2) ≤ m (G) and any convex function f : R ≥ 0 → R with f (0) = 0 . Here ϕ ∗ is the rearrangement of ϕ . Let Y O (P , G) and Y R (P , G) denote the optimal constants of Young’s and the reverse Young’s inequality, respectively, under the assumption μ (supp ϕ 1) + μ (supp ϕ 2) ≤ m (G) . Then we have Y O (P , G) ≤ Y O (P , R) and Y R (P , G) ≥ Y R (P , R) as a corollary. Thus, we obtain that m (G) = ∞ if and only if H (p , G) ≤ H (p , R) in the case of p ′ : = p / (p - 1) ∈ 2 Z , where H(p, G) is the optimal constant of the Hausdorff–Young inequality. [ABSTRACT FROM AUTHOR]

In this article, the main objective is construction of fractional Newton–Simpson-type inequalities with the concept of majorization. We established a new identity on estimates of definite integrals utilizing majorization and this identity will lead us to develop new generalized forms of prior estimates. Some basic inequalities such as Hölder's, power-mean, and Young's along with the Niezgoda–Jensen–Mercer inequality have been used to obtain new bounds and it has been determined that the main findings are generalizations of many results that exist in the literature. Applications to the quadrature rule are given as well. We make links between our findings and a number of well-known discoveries in the literature. [ABSTRACT FROM AUTHOR]

This paper originates from a naive attempt to establish various non-commutative Fourier-theoretic inequalities for an inclusion of simple C*-algebras equipped with a conditional expectation of index-finite type. In this setting, we discuss the Hausdorff-Young inequality and Young's inequality. As a consequence, we prove the Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle. Our results generalize some of the results of Jiang, Liu and Wu [Noncommutative uncertainty principle, J. Funct. Anal., 270(1): 264-311, 2016]. [ABSTRACT FROM AUTHOR]

In this article, we introduce the notion of aT¯p;q-integrals. Using the definition of a T¯p;q-integrals, we derive some new post quantum analogues of some classical results of Young's inequality, H¨older's inequality, Minkowski's inequality, Ostrowski's inequality and Hermite-Hadamard's inequality. [ABSTRACT FROM AUTHOR]

In this paper, we prove several new integral inequalities for the k-Hilfer fractional derivative operator, which is a fractional calculus operator. As a result, we have a whole new set of fractional integral inequalities. For the generalized fractional derivative, we also use Young's inequality to find new forms of inequalities. Such conclusions for this novel and generalized fractional derivative are extremely useful and valuable in the domains of differential equations and fractional differential calculus, both of which have a strong connections to real-world situations. These findings may stimulate additional research in a variety of fields of pure and applied sciences. [ABSTRACT FROM AUTHOR]

Fractional calculus has been a concept used to acquire new variants of some well-known integral inequalities. In this study, our primary goal is to develop majorized fractional Simpson’s type estimates by employing a differentiable function. Practicing majorization theory, we formulate a new auxiliary identity by utilizing fractional integral operators. In order to obtain new bounds, we employ the idea of convex functions on the Niezgoda–Jensen–Mercer inequality for majorized tuples, along with some fundamental inequalities including the Hölder, power mean, and Young inequalities. Some applications to the quadrature rule and examples for special functions are provided as well. Interestingly, the main findings are the generalizations of many known results in the existing literature.

The comprehension of inequalities in preinvexity is very important for studying fractional calculus and its effectiveness in many applied sciences. In this article, we develop and study of fractional integral inequalities whose second derivatives are preinvex functions. We investigate and prove new lemma for twice differentiable functions involving Riemann-Liouville(R-L) fractional integral operator. On the basis of this newly developed lemma, we make some new results regarding of this identity. These new results yield us some generalizations of the prior results. This study builds upon on a novel new auxiliary result which enables us to develop new variants of Ostrowski type inequalities for twice differentiable preinvex mappings. As an application, several estimates concerning Bessel functions of real numbers are also illustrated.

Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this article is to acquire new Hermite-Hadamard type inequalities employing the Riemann-Liouville fractional operator for functions whose third derivatives of absolute values are convex and quasi-convex in nature. Some special cases of the newly presented results are discussed as well. As applications, several estimates concerning Bessel functions and special means of real numbers are illustrated.

The aim of this article is to give new generalizations of both the Ostrowski's inequality and some of its new variants with the help of the F-convex function class, which is a generalization of the strongly convex functions. Young's inequality, which is well known in the literature, as well as Hölder's inequality, was used to obtain the new results. Also we obtain some results for convex and strongly convex functions by utilizing these inequalities.

In this paper, we prove some new generalized inequalities of Hilbert-type on time scales nabla calculus by applying Hölder's inequality, Young's inequality, and Jensen's inequality. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we prove that if a, b > 0 and 0 ≤ v ≤ 1. Then for all positive integer m

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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.

Abstract In this paper, we discuss some new Hilbert-type dynamic inequalities on time scales in two separate variables. We also deduce special cases, like some integral and their respective discrete inequalities.

Abstract In this paper, we establish some new integral inequalities involving general kernels. We obtain the related broad range of fractional integral inequalities. Also, we apply the Young inequality to find new forms of inequalities for generalized kernels. These new and motivated results generalize the results for fractional integrals such that fractional integral of a function with respect to an increasing function, Riemann–Lioville fractional integrals, Erdélyi–Kober fractional integrals, Hadamard fractional integrals, generalized factional integral integrals in addition to the corresponding k-fractional integrals.

In this paper we obtain some new inequalities for Heinz operator mean.

In the present paper we establish some new Opial-Wirtinger’s type inequalities involving Katugampola partial derivatives. These new results in special cases yield Agarwal and Pang’s, Traple’s and Pachpatte’s inequalities and provide new estimates on inequality of this type.

In this note, we obtain generalized versions of reverse Young inequalities as follows: For a1,a2, . . . ,an ∈ [m,M] with M ≥ m > 0 v1a1 + v2a2 + ⋯ + vnan ≤ S(M/m) a1v1a2v2 . . . anvn and v1a1 + v1a2 + ⋯ + vnan ≤ maxai∈[ m,M] S(ai/aj) L(ai/aj) + a1v1a2v2 . . . anvn where S(⋅) is Specht's ratio, L(aii,aj) is logarithmic mean and vi ∈ [ 0,1] such that v1 + v2 + ⋅⋅⋅ + vn = 1. Unlike the proof methods used in the articles on Young's inequality, the proofs of this study are obtained through first order conditions for constrained optimization problems. [ABSTRACT FROM AUTHOR]

In this work, we examine the oscillation of a class fractional differential equations in the frame of generalized nonlocal fractional derivatives with function dependent kernel type. We present sufficient conditions to prove the oscillation criteria in both of the Riemann-Liouville (RL) and Caputo types. Taking particular cases of the nondecreasing function appearing in the kernel of the treated fractional derivative recovers the oscillation of several proven results investigated previously in literature. Two examples, where the kernel function is quadratic and cubic polynomial, have been given to support the validity of the proven results for the RL and Caputo cases, respectively. [ABSTRACT FROM AUTHOR]

In this paper we obtain some Yöung and Holder type inequalities for the weighted geometric mean of positive operators on Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this work, by the weighted arithmetic-geometric mean inequality, we show if a,b > 0 and 0 A B 1. Then for all positive integer m, we have where r0 = min{ν,1-ν }, rm = min{2mrm 0, (1-r0)m-rm 0} and χI (ν) the characteristic function. This inequality provides a generalization of an important refinement of the Young inequality obtained by J. Zhao and J. Wu. As applications we give some new generalized refinements of Young type inequalities for the determinants, p-norms and traces, of positive τ -measurable operators. [ABSTRACT FROM AUTHOR]

Abstract In this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed delay and stochastic noise are simultaneously taken into consideration. In order to guarantee the exponential stability of our considered recurrent neural networks, two distinct types of sufficient conditions are derived on the basis of the Lyapunov functional and coefficient of our given system and also to construct a Lyapunov function for a large scale system a novel graph-theoretic approach is considered, which is derived by utilizing the Lyapunov functional as well as graph theory. In this approach a global Lyapunov functional is constructed which is more related to the topological structure of the given system. We present a numerical example and simulation figures to show the effectiveness of our proposed work.

In this paper we establish some multiplicative inequalities for weighted arithmetic and harmonic operator means under various assumption for the positive invertible operators A, B. Some applications when A, B are bounded above and below by positive constants are given as well.