Journal of Inequalities and Applications最新文献

In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those sums of finite products in terms of Bernoulli polynomials and obtain some identities by using those expressions.

A two-point Padé approximant method is presented for refining some remarkable trigonometric inequalities including the Jordan inequality, Kober inequality, Becker-Stark inequality, and Wu-Srivastava inequality. Simple proofs are provided. It shows to achieve better approximation results than those of prevailing methods.

Recently we have introduced a product-type operator and studied it on some spaces of analytic functions on the unit disc. Here we start investigating the operator on the space of analytic functions on the upper half-plane. We characterize the boundedness and compactness of the operator between Hardy and α-Bloch spaces on the domain.

In the present paper, we investigate majorization properties for the class $M_{\beta }^{\alpha }(p,\gamma )$ of uniformly starlike functions and the class $N_{\beta }^{\alpha }(p,\theta )$ of spiral-like functions related to an exponential function, which are defined through the Liu-Owa integral operator $Q_{\beta ,p}^{\alpha }$ given by (1.5). Also, some special cases of our main results in a form of corollaries are shown.

The Jacobian decomposition and the Gauss-Seidel decomposition of augmented Lagrangian method (ALM) are two popular methods for separable convex programming. However, their convergence is not guaranteed for three-block separable convex programming. In this paper, we present a modified hybrid decomposition of ALM (MHD-ALM) for three-block separable convex programming, which first updates all variables by a hybrid decomposition of ALM, and then corrects the output by a correction step with constant step size $\alpha \in (0,2-\sqrt{2})$ which is much less restricted than the step sizes in similar methods. Furthermore, we show that $2-\sqrt{2}$ is the optimal upper bound of the constant step size α. The rationality of MHD-ALM is testified by theoretical analysis, including global convergence, ergodic convergence rate, nonergodic convergence rate, and refined ergodic convergence rate. MHD-ALM is applied to solve video background extraction problem, and numerical results indicate that it is numerically reliable and requires less computation.

In this paper, we introduce a new kind of approximate weakly efficient solutions to the set-valued vector equilibrium problems with constraints in locally convex Hausdorff topological vector spaces; then we discuss a relationship between the weakly efficient solutions and approximate weakly efficient solutions. Under the assumption of near cone-subconvexlikeness, by using the separation theorem for convex sets we establish Kuhn-Tucker-type and Lagrange-type optimality conditions for set-valued vector equilibrium problems, respectively.

This paper considers wavelet estimation for a multivariate density function based on mixing and size-biased data. We provide upper bounds for the mean integrated squared error (MISE) of wavelet estimators. It turns out that our results reduce to the corresponding theorem of Shirazi and Doosti (Stat. Methodol. 27:12-19, 2015), when the random sample is independent.

In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by $n(a,B)$ and $n(a,E)$ , respectively. Secondly, we derive the mean value of a positive logarithm of generating functions of Bernoulli numbers and associated Euler numbers shown as $m(2\pi ,B)$ and $m(\pi ,E)$ , respectively. From these properties, we find Nevanlinna characteristic functions which we stated in the paper. Finally, as an application, we show that the generating function of Bernoulli numbers is a normal function.

The construction of bi-frames is a fundamental problem in frame theory. Due to their wide applications, the study of vector-valued frames and subspace frames has interested many mathematicians in recent years. In this paper, we introduce the weak Gabor bi-frame (WGBF) in vector-valued subspaces, characterize WGBFs on the time domain, and present some examples.

In this paper, we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents and inequalities with certain polynomial exponents. Also, we establish intervals in which these inequalities hold.