Related papers: Revisiting a sharpened version of Hadamard's deter…
In 1992, Goulden and Jackson found a beautiful determinantal expression for the immanant of a matrix. This paper proves the same result combinatorially.
The main goal of this article is to present several quadratic refinements and reverses of the well known Heinz inequality, for numbers and matrices, where the refining term is a quadratic function in the mean parameters. The proposed idea…
In this article we establish new improvements of the optimal Hardy inequality in the half space. We first add all possible linear combinations of Hardy type terms thus revealing the structure of this type of inequalities and obtaining best…
Some refinements of the Hermite-Hadamard inequality are obtained in the case of continuous convex functions defined on simplices.
In this paper we improve a result recently proved by Irshad et al. [On the Inequalities Concerning to the Polar Derivative of a Polynomial with Restricted Zeroes, Thai Journal of Mathematics, 2014 (Article in Press)] and also extend…
We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our arguments build on certain weighted inequalities based on…
In this paper, we establish some new Hadamard type inequalities using elementary well known inequalities for functions whose inequalities absolute values are {\alpha}-, m-, ({\alpha},m)-logarithmically convex.
Certain rearrangement inequalities of a type considered by Hardy, Riesz, and Brascamp-Lieb-Luttinger are studied. Subsets of the real line that extremize these inequalities are characterized. Our results apply only to special cases, and…
We derive identities for the determinants of matrices whose entries are (rising) powers of (products of) polynomials that satisfy a recurrence relation. In particular, these results cover the cases for Fibonacci polynomials, Lucas…
Wang and Yau [10] introduced a quasi-local mass, which is a hyperbolic background generalization of Liu-Yau's expression [7] [8], and proved its positivity. In this note, we prove that the positivity of this quasi-local mass is still valid…
We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the…
The Riccati equation method is used to establish new oscillation criteria for extended linear matrix Hamiltonian systems. This method allows to obtain results in in a new direction, which is to break the positive definiteness condition,…
The purpose of this paper is to revisit the proof of the Gearhardt-Pr\"uss-Hwang-Greiner theorem for a semigroup $S(t)$, following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on $\Vert…
This paper is concerned with long-time dynamics of semilinear wave equations defined on bounded domains of $\mathbb{R}^3$ with cubic nonlinear terms and locally distributed damping. The existence of regular finite-dimensional global…
We prove some new retarded integral inequalities. The results generalize those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].
In this paper, is introduced a new proposal of resolvent for equilibrium problems in terms of the Busemann's function. A great advantage of this new proposal is that, in addition to be a natural extension of the proposal in the linear…
By applying results obtained from the new versions of the classical Levy, Ottaviani, and Hoffmann-Jorgensen (1974) inequalities proved by Li and Rosalsky(2013) and by using techniques developed by Hechner and Heinkel (2010), we provide a…
Recently, Borodin and Okounkov established a remarkable identity for Toeplitz determinants. Two other proofs of this identity were subsequently found by Basor and Widom, who also extended the formula to the block case. We here give one more…
In this paper, we not only give the extensions of the results given in [7] by Gill et al. for log-convex functions, but also obtain some new Hadamard type inequalities for log-convex, m-convex and (alpha,m)-convex functions.
Hayashi's Pinching Inequality, which establishes a matrix inequality between a semidefinite matrix and a multiple of its "pinched" version via a projective measurement, has found many applications in quantum information theory and beyond.…