Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.

ON PROBLEM OF NEAREST COMMON FIXED POINT OF NONEXPANSIVE MAPPINGS

The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.

SET-VALUED CARISTI’S FIXED POINT THEOREM AND EEELAND’S VARIATIONAL PRINCIPLE

This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].

Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem

By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .

无电离层组合、Uofc和非组合精密单点定位观测模型比较

GNSS精密单点定位技术因其只采用单台接收机就能获得高精度的定位结果而成为近年来的研究热点。精密单点定位通常采用3种模型:无电离层组合模型、Uofc模型与非组合模型。本文从模糊度固定的角度详细论述了这3种模型的相互关系,公式推导证明了非组合模型与Uofc模型等价,且都优于无电离层组合模型;与采用等价性原理消去电离层延迟的Uofc模型相比,非组合模型将电离层延迟作为参数求解,能为用户提供附加电离层先验约束的条件,从而方便地转换为电离层加权模型。在固定宽巷模糊度的情况下,采用模糊度精度因子(ADOP)对模糊度的固定效率进行了分析,验证了Uofc模型相对于无电离层组合模型具有噪声小、不损失原始观测信息等优点。而附电离层约束的非组合模型在高精度先验电离层信息约束下能有效提高模糊度固定效率。

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

Oscillation in a Class of Neutral Differential Equations with Positive and Negative Coefficients

The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.

CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve the corresponding results of [1, 2, 4-9, 11-15].

PROBLEM OF PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

The problem of periodic solutions for a kind of kth-order linear neutral functional differential equation is studied. By using the theory of Fourier expansions, a sufficient and necessary condition to guarantee the existence and uniqueness of periodic solution is obtained. Further, by applying this result and Schauder's fixed point principle, a kind of kth-order nonlinear neutral functional differential equation is investigated, and some new results on existence of the periodic solutions are given as well. These results improve and extend some known results in recent literature.

A Variational Principle in Probabilistic Metric Spaces(Ⅱ)~* 概率度量空间中的变分原理

本文研究概率度量空间中的变分原理.我们证明了概率分析中的一个序原理,应用这个序原理并引入分布值映射的下半连续性概念,把Ekeland变分原理和Caristi不动点定理推广到概率度量空间中.

Uncertainty Principle and Bifurcations in the SU(2) Nonlinear Semiquantum Dynamics

In this paper, a nonlinear semiquantum Hamiltonian associated to the special unitary group SU(2) Lie algebra is studied so as to analyze its dynamics. The treatment here applied allows for a reduction in: 1) the system’s dimension, as well as 2) the number of system’s parameters (to only three). We can now discern clear patterns in: 1) the complete characterization of the system’s fixed points and 2) their stability. It is shown that the parameter associated to the uncertainty principle, which constitutes a very strong constraint, is the key one in determining the presence of fixed points and bifurcation curves in the parameter’s space.

A Kind of Boundary Value Problems for Stochastic Differential Equations

In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and Leray-Schauder fixed point theorem, respectively.

THE NONEMPTINESS AND COMPACTNESS OF MILD SOLUTION SETS FOR RIEMANN-LIOUVILLE FRACTIONAL DELAY DIFFERENTIAL VARIATIONAL INEQUALITIES

This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities,which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality.Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.

A Kind of Nonconvex-valued Functional Differential Inclusions Problems

In this paper,we consider nonconvex-valued functional differential inclusions with nonlinear semigroups in Banach spaces,the existence of the integral solutions is proved.

A Generalization of Caristi's Fixed Point Theorem and Its Applications

The paper generalizes the classical Caristi＇s fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi＇s fixed point theorem is equivalent to the generalized Ekeland variational principle.

具有积分边界条件的耦合φ-Hilfer分数阶微分系统解的存在性

为了拓展分数阶微分方程系统的相关理论,研究了一类具有积分边界条件的耦合φ-Hilfer分数阶微分系统。首先,将具有积分边界条件的耦合φ-Hilfer分数阶微分系统转化为积分系统;其次,定义合适的Banach乘积空间和范数,构造合适的积分算子,分别运用压缩映像原理和Kransnoselskii不动点定理得出耦合φ-Hilfer分数阶微分系统在积分边界条件下解的存在性结果;最后,通过列举实例说明所得结论的正确性。研究表明,积分边界条件下的耦合φ-Hilfer分数阶微分系统的解具有存在性。研究结论丰富了耦合分数阶微分系统理论可解性的相关理论,可为深入研究分数阶微分方程提供一定的理论参考。

一类非线性混合分数阶微分方程系统解的稳定性

研究了一类含Caputo型非线性混合分数阶微分方程耦合系统的边值问题,首先,利用Banach压缩映射原理讨论了该系统解的存在唯一性,并利用Dhage不动点定理研究了该系统解的存在性;然后,研究了该系统解的Ulam-Hyers稳定性、G-Ulam-Hyers稳定性和Ulam-Hyers-Rassia稳定性,并利用算例验证了所得结果的正确性.

EKELAND'S VARIATIONAL PRINCIPLE AND CARISTI'S FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE

The main purpose of this paper is to establish the Ekeland’s variational principle andCaristi’s fixed point theorem in probabilistic metric spaces and to give a direct simple proofof the equivalence between these two theorems in the probabilistic metric space. The resultspresented in this paper generalize the corresponding results of [9--12].

一类带参数的超线性椭圆型方程边值问题的可解性

本文研究了一类椭圆型方程Dirichlet边值问题的可解性,其中,非线性项包含了线性部分、参数及在无穷远处为超线性的部分。利用不动点定理及上下解方法来证明了该问题在参数λ充分小时正解的存在性;在非线性项满足Lipschitz连续及参数λ充分小时解的唯一性定理;同时论证了在一定条件下解的不存在性定理。最后分别给出了定理的应用实例。

概反周期函数及其在一类Hopfield神经网络上的应用

探讨一类具有混合时滞的中立型Hopfield神经网络的概反周期解的存在性与稳定性。首先,讨论了概周期函数与概反周期函数之间的关系,证明了全体概反周期函数构成的集合,是概周期函数空间的一个闭子空间。最后,利用不动点原理得到Hopfield神经网络存在一个唯一的有界解,而且该解函数还是概反周期函数。概反周期函数是比概周期函数更精细的函数,对神经网络概反周期解的存在性与唯一性的探讨,相较于对概周期解的存在性以及唯一性的探讨,能够更加精确地描述神经网络的动力学性质,所得结论是新颖的,是现有结论的进一步完善与补充。