Journal of Inequalities and Applications最新文献

We present two classes of asymptotic expansions related to Somos' quadratic recurrence constant and provide the recursive relations for determining the coefficients of each class of the asymptotic expansions by using Bell polynomials and other techniques. We also present continued fraction approximations related to Somos' quadratic recurrence constant.

In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral. Moreover, using the obtained results, we give a new generalization of the Minkowski inequality for the triple Diamond-Alpha integral on time scales.

This paper studies the admissibility of simultaneous prediction of actual and average values of the regressand in the generalized linear regression model under the quadratic loss function. Necessary and sufficient conditions are derived for the simultaneous prediction to be admissible in classes of homogeneous and nonhomogeneous linear predictors, respectively.

In this paper, we first prove an integral majorization theorem related to integral inequalities for functions defined on rectangles. We then apply the result to establish some new integral inequalities for functions defined on rectangles. The results obtained are generalizations of weighted Favard's inequality, which also provide a generalization of the results given by Maligranda et al. (J. Math. Anal. Appl. 190:248-262, 1995) in an earlier paper.

For $1\le p<n$ , the embeddings of Sobolev spaces $W_{\Delta }^{1,p}\left({\Omega }_{T^n}\right)$ of functions defined on an open subset of an arbitrary time scale $T^n$ , $n\ge 1$ , endowed with the Lebesgue Δ-measure have been developed in (Agarwal et al. in Adv. Differ. Equ. 2006:38121, 2006) for $n=1$ and later generalized to arbitrary $n\ge 1$ in (Su et al. in Dyn. Partial Differ. Equ. 12(3):241-263, 2015). In this article we present the embeddings of Sobolev spaces $W_{\Delta }^{1,p}\left({\Omega }_{T^n}\right)$ for $n\le p\le \infty$ and then, using these embeddings, we develop general Sobolev's embedding for the Sobolev spaces $W_{\Delta }^{1,p}\left({\Omega }_{T^n}\right)$ on time scales, where k is a non-negative integer and $1\le p\le \infty$ .

By utilizing the concept of generalized order, we investigate the growth of Laplace-Stieltjes transform converging in the half plane and obtain one equivalence theorem concerning the generalized order of Laplace-Stieltjes transforms. Besides, we also study the problem on the approximation of this Laplace-Stieltjes transform and give some results about the generalized order, the error, and the coefficients of Laplace-Stieltjes transforms. Our results are extension and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava.

In this paper, we prove almost-Schur inequalities on closed smooth metric measure spaces, which implies the results of Cheng and De Lellis-Topping whenever the weighted function f is constant.

In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by using the backward Euler scheme in time. Moreover, by using an orthogonal projection operator, we obtain $L^2\left(H^1\right)-L^2\left(L^2\right)$ a posteriori error estimates of the approximation solutions for both the state and the control. Finally, by introducing two auxiliary equations, we also obtain $L^2\left(L^2\right)-L^2\left(L^2\right)$ a posteriori error estimates of the approximation solutions for both the state and the control.

Based on a recent paper of Beg and Pathak (Vietnam J. Math. 46(3):693-706, 2018), we introduce the concept of $H_q^{+}$ -type Suzuki multivalued contraction mappings. We establish a fixed point theorem for this type of mappings in the setting of complete weak partial metric spaces. We also present an illustrated example. Moreover, we provide applications to a homotopy result and to an integral inclusion of Fredholm type. Finally, we suggest open problems for the class of 0-complete weak partial metric spaces, which is more general than complete weak partial metric spaces.

We establish some new noninstantaneous impulsive inequalities using the conformable fractional calculus.