Journal of Inequalities and Applications最新文献

In this paper we prove the Hadamard and the Fejér-Hadamard inequalities for the extended generalized fractional integral operator involving the extended generalized Mittag-Leffler function. The extended generalized Mittag-Leffler function includes many known special functions. We have several such inequalities corresponding to special cases of the extended generalized Mittag-Leffler function. Also there we note the known results that can be obtained.

Saddle-point problems arise in many areas of scientific computing and engineering applications. Research on the efficient numerical methods of these problems has become a hot topic in recent years. In this paper, we propose some generalizations of the new SOR-like method based on the original method. Convergence of these methods is discussed under suitable restrictions on iteration parameters. Numerical experiments are given to show that these methods are effective and efficient.

In this paper, we provide a new quicker sequence convergent to the Euler-Mascheroni constant using an approximation of Padé type. Our sequence has a relatively simple form and higher speed of convergence. Moreover, we establish lower and upper bound estimates for the difference between the sequence and the Euler-Mascheroni constant.

In this paper, we generalize the concept of well-posedness to a class of split hemivariational inequalities. By imposing very mild assumptions on involved operators, we establish some metric characterizations of the well-posedness for the split hemivariational inequality. The obtained results generalize some related theorems on well-posedness for hemivariational inequalities and variational inequalities in the literature.

Consider the linear regression model $y_i=x_i^T\beta +e_i,i=1,2,\dots ,n,$ where $e_i=g(\dots ,{\epsilon }_{i-1},{\epsilon }_i)$ are general dependence errors. The Bahadur representations of M-estimators of the parameter β are given, by which asymptotically the theory of M-estimation in linear regression models is unified. As applications, the normal distributions and the rates of strong convergence are investigated, while $\{{\epsilon }_i,i\in Z\}$ are m-dependent, and the martingale difference and $(\epsilon ,\psi )$ -weakly dependent.

In the paper, the authors present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as Chebychev's inequality for synchronous (or asynchronous, respectively) mappings, give a new proof of the log-convexity of the extended gamma function by using the Hölder inequality, and introduce a Turán type mean inequality for the Kummer confluent k-hypergeometric function.

In this paper, we will show some improvements of Heron mean and the refinements of Young's inequalities for operators and matrices with a different method based on others' results.

In this paper, we extend some known results about complete convergence and establish the complete convergence and complete moment convergence for randomly weighted sums of martingale difference sequence. Our results can generalize some conclusions related to Hsu-Robbins-Erdös strong laws and Baum-Katz type theorems for martingales.

The main purpose of this paper is applying the analysis method, the properties of Lucas polynomials and Gauss sums to study the estimation problems of some kind hybrid character sums. In the end, we obtain several sharp upper bound estimates for them. As some applications, we prove some new and interesting combinatorial identities.

In this paper, based on $(\alpha ,m)$ -convexity, we establish different type inequalities via quantum integrals. These inequalities generalize some results given in the literature.