一般化凸空间上的几乎不动点, 不动点和拟变分不等式

The definitions of S-KKM property and Γ-invariable property for multi-valued map- ping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uniform space are obtained, and a quasi-variational inequality theorem for acyclic map on Hausdorff Φ-space is proved. Our results improve and generalize the corresponding results in recent literatures.     

A general multi-valued hybrid fixed point theorem and perturbed differential inclusions

Combining three basic multi-valued versions of Banach, Schauder and Tarski fixed point theorems, a general hybrid fixed point theorem for multi-valued mappings in Banach spaces is proved via measure of noncompactness and it is further applied to perturbed differential inclusions for proving the existence results under mixed Lipschitz, compactness and monotone conditions.     

General auxiliary problem and algorithm for a generalized multi-valued variational-like inequality problem in reflexive Banach spaces

In this article, some generalized multi-valued variational-like inequality problems and their related general auxiliary problems in real reflexive Banach spaces are introduced. An existence theorem for one of the general auxiliary problems is proved. Furthermore, by exploiting this theorem, an algorithm for the corresponding generalized multi-valued variational-like inequality problem is constructed. The theorems of this article generalize, improve and unify many known corresponding results.     

Generalizations of theorems of J. Aczél and R. Ger and T. Kochanek

Periodica Mathematica Hungarica - We present a result which generalizes a theorem proved by Aczél (Bull Am Math Soc 54:392–400, 1948). Hence we obtain generalizations of a theorem proved...     

Asymptotic expansions for parabolic systems

We consider a parabolic system in a half space. A theorem, similar to one proved by Meyers and Pazy for elliptic equations outside the unit ball is proved, namely, if the coefficients, the right side, and the initial conditions of the parabolic system have asymptotic expansions at infinity with respect to the space variable, then so does the solution of the corresponding Cauchy problem. Some generalizations and examples are given.     

Some results for fractional boundary value problem of differential inclusions

In this paper, we study fractional differential inclusions with Dirichlet boundary conditions. We prove the existence of a solution under both convexity and nonconvexity conditions on the multi-valued right-hand side. The proofs rely on nonlinear alternative Leray–Schauder type, Bressan–Colombo selection theorem and Covitz and Nadler’s fixed point theorem for multi-valued contractions. The compactness of the set solutions and relaxation results is also established. In the last section we consider the fractional boundary value problem with infinite delay.     

Mizoguchi–Takahashi’s type common fixed point theorem

Recently Kamran extended the result of Mizoguchi and Takahashi for closed multi-valued mappings and proved a fixed point theorem. In this paper we further extend the result concluded by Kamran and prove a common fixed point theorem by using the concept of lower semi-continuity.     

希尔伯特空间上的李雅普诺夫定理

我们用■(C)记n维欧氏空间 C~n 上的 n×n 阶矩阵全体,其中自共轭矩阵全体记为■_n.关于矩阵的 Lyapunov 定理和 Stein 定理通常分别叙述成Lyapunov 定理.对矩阵 A∈■(C),存在一自共轭矩阵 x∈■_n,且 X>0(正定),使 AX XA~*>0的充要条件是 A 的特征值完全落在复平面的右半开平面内.这里 A~*表示 A 的转置共轭矩阵,而右半开平面是指不包含虚轴的右半平面.     

Some new results and generalizations in metric fixed point theory

The main purpose of this paper is the study of the generalization of some results given in [M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. 326 (2007) 772-782] and references therein. Some generalizations of the Mizoguchi-Takahashi fixed point theorem, Kannan’s fixed point theorems and Chatterjea’s fixed point theorems are established by using our new fixed point theorems.     

Degree of rational mappings, and the theorems of Sturm and Tarski

We provide an explicit algorithm of computing the mapping degree of a rational mapping from the real projective line to itself. As a corollary we prove Sturm’s theorem and a number of its generalizations. These generalizations are used to prove Tarski’s theorem about real semialgebraic sets. Similarly a version of Tarski’s theorem can be proved for an arbitrary algebraically closed field. To V. I. Arnold on the occasion of his 70th birthday     

一类时滞依赖状态的集值抽象积分微分方程的可解性

本文研究了一类时滞依赖状态的集值抽象积分微分方程的可解性问题.利用集值映射不动点定理结合分析预解算子理论的方法,证明了上述微分方程温和解的存在性,推广了现有集值微分方程的结果.     

Common fixed point theorem for cyclic generalized multi-valued contraction mappings

In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multi-valued mappings.     

Clifford algebra approach to pointwise convergence of Fourier series on spheres Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We offer an approach by means of Clifford algebra to convergence of Fourier series on unit spheres of even-dimensional Euclidean spaces. It is based on generalizations of Fueter's Theorem inducing quaternionic regular functions from holomorphic functions in the complex plane. We, especially, do not rely on the heavy use of special functions. Analogous Riemann-Lebesgue theorem, localization principle and a Dini's type pointwise convergence theorem are proved.     

General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group Cr(P k n ) of Birational Transformations

A general approach is developed for integrating an invertible dynamical system defined by the composition of two involutions, i.e., a nonlinear one which is a standard Cremona transformation, and a linear one. By the Noether theorem, the integration of these systems is the foundation for integrating a broad class of Cremona dynamical systems. We obtain a functional equation for invariant homogeneous polynomials and sufficient conditions for the algebraic integrability of the systems under consideration. It is proved that Siegel's linearization theorem is applicable if the eigenvalues of the map at a fixed point are algebraic numbers.     

Multi-valued contraction mappings in generalized metric spaces

Several fixed point theorems for multi-valued global and local contraction mappings are proved. These results concerning contractions are then applied to obtain a fixed point theorem for a certain type of single-valued locally expansive mapping.     

Approximately solving multi-valued variational inequalities by using a projection and contraction algorithm

A projection and contraction algorithm for solving multi-valued variational inequalities is proposed. The algorithm is proved to converge globally to a solution of a given multi-valued variational inequality under standard conditions. We present an analysis of the convergence rate. Finally, preliminary computational experiments illustrate the advantage of the proposed algorithm.     

Maximal branching processes with several types of particles

The paper introduces multitype maximal branching processes and their generalizations. Some examples of their explicit construction are given. The ergodic theorem is proved for the case of two types of particles.     

Two concepts of singularity for matrices over semirings

The two common concepts of singularity for matrices over semirings are being studied since the 1970’s and arise from natural generalizations of the determinant and linear dependence. They were introduced in the context of schedule algebras by Gondran and Minoux, who proved later that the concepts discussed are equivalent over any selective invertible semiring. We present an approach that uses a generalization of power series arithmetic and, in particular, allows to derive a short proof for the theorem of Gondran and Minoux. Our main result is a complete concise characterization of semirings over which the two concepts of singularity are equivalent.     

集值映象的向量变分不等式和相补问题

研究了一类集值映象的广义向量变分不等式和相补问题 ,证明了解的一些存在性定理 .推广和改进了文 [1 ,4 6 ]的相关研究成果 .     

Solvability of impulsive neutral evolution differential inclusions with state-dependent delay

In this paper, we prove the existence of mild solutions for a first order impulsive neutral evolution differential inclusion with state-dependent delay. We transform it into an integral equation and use a fixed point theorem for condensing multi-valued maps. As an application of the main theorem, we consider the case when the multi-valued nonlinearity has sub-linear growth in the state variable.