SANDWICH-TYPE THEOREMS FOR MEROMORPHIC MULTIVALENT FUNCTIONS ASSOCIATED WITH THE LIU-SRIVASTAVA OPERATOR＊

The purpose of this article is to obtain some subordination and superordination preserving properties of meromorphic multivalent functions in the punctured open unit disk associated with the Liu-Srivas...     

A new lower bound of the Hausdorff measure of the Sierpinski gasket

For the Sierpinski gasket, by using a sort of cover consisting of special regular hexagons, we define a new measure that is equivalent to the Hausdorff measure and obtain a lower bound of this measure. Moreover, the following lower bound of the Hausdroff measure of the Sierpinski gasket has been achieved H^s（S）≥0.670432,where S denotes the Sierpinski gasket, s = dimn（S） = log23, and H^s（S） denotes the s-dimensional Hausdorff measure of S. The above result improves that developed in .     

A new condition for certain trigonometric series

The present paper proposes a new natural weak condition to replace the quasimonotone and O-regularly varying quasimonotone conditions, and shows the conclusion of the main result in [10] still holds. Moreover, we prove that any O-regularly varying quasimonotone condition implies this condition, thus tne vague implication of quasimonotonicity can be avoided in practice.     

A generalized iterative method and comparison results using projection techniques for solving linear systems

In [Y.-F. Jing, T.-Z. Huang, On a new iterative method for solving linear systems and comparison results, J. Comput. Appl. Math. 220 (2008) 74–84], Jing and Huang obtained a new iterative method for solving linear systems. This method can be considered as a projection method which uses a two-dimensional space at each step. In this paper, we generalize this method to a three-dimensional projection process. And a different approach is established, which is both theoretically and numerically proven to be better than (or at least the same as) [Jing and Huang’s (2008)].     

关于Liu-Owa积分算子的双重从属保持性质

本文研究了单位圆盘内关于Liu-Owa积分算子的多叶解析函数类的从属和超从属保持问题.利用微分从属的方法,获得了该类函数的中间型结果,推广和改进了一些已知结果.     

On a nonhomogeneous,nonlinear Dirichlet eigenvalue problem

We consider a nonlinear eigenvalue problem for the Dirichlet $(p,q)$-Laplacian with a sign-changing Carath$\acute{\mathrm{e}}$odory reaction. Using variational tools, truncation and comparison techniques, and critical groups, we prove an existence and multiplicity result which is global in the parameter $\lambda >0$ (bifurcation-type theorem). Our work here complements the recent one by Papageorgiou–Qin–Rădulescu, Bull. Sci. Math. 172 (2021).