凸函数及其在概率论中的应用

本文主要讨论了凸函数的某些性质,有些结果是已知的,伹我们给出了简短的证明并获得了凸函数的一些新的性质,然后讨论了凸函数在概率论中的一些应用,并获得了一些新的结果。     

关于一类含有Dziok-Srivastava算子的多叶解析函数的包含关系和卷积性质

该文引进和研究了一类含有Dziok-Srivastava算子的新的多叶解析函数. 得到了这一函数类中的一些有趣的性质, 如包含关系, 卷积性质等. 这些结果改进和拓展了早期的一些工作. 同时也得到了其他一些新的结果.     

拓扑空间中的KKM型定理和重合点定理

引入了一类新的有限连续空间(简称, $FC$-空间),并在$FC$-空间中证明了一些新的涉及容许类集值映射和具有紧局部交性质的KKM型定理和重合点定理.作为应用,在$FC$-空间中得到了一些新的不动点定理.这些结果统一和推广了近期文献在抽象凸空间中的一些重要结果.     

G-凸空间中的KKM定理，匹配定理和截口定理

在G-凸空间中证明了一些新的KKM型定理．作为应用,在G-凸空间中得到了一些新的匹配定理和截口定理,所得结果改进和推广了[2,3,7]中的相关结果．     

Banach空间上的Banach框架及原子分解的稳定性

讨论了Banach空间上的Banach框架及原子分解的稳定性,得到了一些新的结果,并给出一些已知结果的推论.     

两两NQD列的强稳定性

该文研究了两两NQD列的强稳定性, 获得了一些新的稳定性结果, 推广了一些在独立情形时已有的结果.     

一类具多偏差变元的p-Laplacian方程周期解的存在性

研究了一类具多偏差变元的p-Laplacian方程,为了得到该方程周期解的先验估计,运用分析技巧建立了一些新的不等式,进而利用Mawhin连续定理得到了这类方程周期解的存在性,得到了一些新的结果,推广和改进了已有结果.     

星像与强星像的某些充分条件(英文)

本文研究了与某些新的函数表达式相关的一些微分不等式及一阶微分从属关系的问题.利用微分从属的方法,获得了一些新的函数星像性与强星像性的充分条件,推广和改进了已有的一些结果.     

NOD随机变量阵列加权乘积和的完全收敛性

利用NOD随机变量的性质,研究了行为NOD随机变量阵列加权乘积和的完全收敛性,获得了一些新的结果,所得的结果推广和改进了已知的一些文献中的一系列结果.     

关于极小极大原理

通过减弱条件,获得了一个新的结果。由此,我们给出一些新的极小极大定理和极小极大不等式。     

图的因子和因子分解的若干进展

本文综述了图的的因子和因子分解近年来的一些新结果。主要有图的因子与各种参数之间的关系,图有某种因子的一些充分必要条件,特别是图有ｋ－因子的一些充分条件以及关于图的因子分解和正交因子分解的一些新结果。文中提出了一些新的问题和猜想。     

Lyapunov-type inequalities for a class of higher-order linear differential equations with anti-periodic boundary conditions

In this paper, we obtain some new Lyapunov-type inequalities for a class of higher-order linear differential equations with anti-periodic boundary value condition, the results of this paper are new and generalize and improve some early results in the literature.     

Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects

This paper deals with a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments by employing a fixed point theorem in cones. Easily verifiable sufficient criteria are established. The paper extends some previous results and reports some new results about impulsive functional differential equations.     

Nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups

In this paper, we consider a class of resonant cooperative elliptic systems. Based on some new results concerning the computations of the critical groups and the Morse theory, we establish some new results about the existence and multiplicity of solutions under new classes of conditions. It turns out that our main results sharply improve some known results in the literature.     

Vector-valued perturbed equilibrium problems

The goal of this paper is to prove some general vector-valued perturbed equilibrium principles and some existence results of vector equilibrium points for bifunctions satisfying a new natural notion of lower semi-continuity. We obtain these results by going through a new concept of approximative equilibrium point.     

New results on the global asymptotic stability of?a?Lotka-Volterra system

In this paper, we revisit the famous Lotka-Volterra competitive system. By combining spectral matrix theory with Lyapunov function, some new sufficient conditions are obtained to guarantee the global asymptotic stability of a unique equilibrium for Lotka-Volterra competitive system. Our new results generalize and significantly improve the known results in the previous literature. The main purpose of this paper is to propose a new methodology to study the high-dimensional Lotka-Volterra system. And this method can be extensively used to study the global asymptotic stability of the equilibrium. Finally, some examples and their simulations show the feasibility and effectiveness of our results.     

New Lyapunov‐type inequalities for a class of even‐order linear differential equations

In this paper, we obtain some new Lyapunov‐type inequalities for a class of even‐order linear differential equations, the results are new and generalize and improve some early results in this field.     

A new approach to improve the order of approximation of the Bernstein operators: theory and applications

This paper presents a new approach to improve the order of approximation of the Bernstein operators. Three new operators of the Bernstein-type with the degree of approximations one, two, and three are obtained. Also, some theoretical results concerning the rate of convergence of the new operators are proved. Finally, some applications of the obtained operators such as approximation of functions and some new quadrature rules are introduced and the theoretical results are verified numerically.     

ON CERTAIN CLASS OF ANALYTIC FUNCTIONS DEFINED BY DIFFERENTIAL SUBORDINATION

In this paper, the new subclass Bn( ,a,A,B) of analytic functions is introduced. Its subordination relations, inclusion relations, the inequality properties and convering theorem are discussed. The results obtained in this paper are sharp, which generalize the related works of some authors and some other new results are obtained.     

Multiplicity of positive solutions to period boundary value problems for second order impulsive differential equations

This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem in cones. The paper extends some previous results and reports some new results about impulsive differential equations.