Banach空间中单值非扩张映射和多值非扩张映射公共不动点混合迭代逼近研究

引入了两个单值非扩张映射与两有限族多值非扩张映射新的混合迭代,在Banach空间中,研究了两个单值非扩张映射与两有限族多值非扩张映射在新迭代下关于公共不动点的收敛性,改进和推广了已有文献相关的结果.     

On the integral characterization of some generalized quasiregular mappings and the significance of the conditions of divergence of integrals in the geometric theory of functions

The paper deals with the theory of space mappings. For a generalization of quasiregular mappings important for the investigation of the Sobolev and other known classes of mappings, we propose a simple condition satisfied by all mappings of this kind and only by these mappings. On the basis of conditions of divergence of the integrals, we establish sufficient conditions for the normality of the families of the analyzed classes of mappings and solve the problem of removing isolated singularities. Some applications of the obtained results to mappings from the Sobolev class are discussed.     

On coincidences of families of mappings on ordered sets

New results on fixed points and coincidences of families of set-valued mappings of partially ordered sets obtained without commutativity assumptions are presented. These results develop theorems on fixed points of an isotone self-mapping of an ordered set (for families of set-valued mappings) and theorems about coincidences of two set-valued mappings one of which is isotone and the other is covering (for finite families of set-valued mappings).     

多复变数一类α次星形映射齐次展开式各项的精细估计

本文首先给出复Banach空间单位球上一类α次星形映射齐次展开式各项的精细估计,特别当这些映射又是k折对称映射时,估计还是精确的.其次建立C~n中单位多圆柱上上述推广映射齐次展开式各项的精细估计,同样当这些映射又是k折对称映射时,估计仍是精确的.由此证明了多复变数中关于α次星形映射的弱Bieberbach猜想,且所得到的估计都能回到单复变数的情形.     

Refined Hyers-Ulam approximation of approximately Jensen type mappings

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved this problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we generalize the Hyers result for the Ulam stability problem for Jensen type mappings, by considering approximately Jensen type mappings satisfying conditions weaker than the Hyers condition, in terms of products of powers of norms. This process leads to a refinement of the well-known Hyers-Ulam approximation for the Ulam stability problem. Besides we introduce additive mappings of the first and second form and investigate pertinent stability results for these mappings. Also we introduce approximately Jensen type mappings and prove that these mappings can be exactly Jensen type, respectively. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.     

A new iterative process for approximating common fixed points of nonself I-asymptotically quasi-nonexpansive mappings

In this paper, we introduce an iterative process for two nonself I-asymptotically quasi-nonexpansive mappings and two finite families of such mappings in Banach spaces, and prove some strong convergence theorems for such mappings. Our results extend some existing results.     

Hartogs域上延拓算子的性质

主要研究Roper-Suffridge延拓算子在推广的Hartogs域上的性质.借助双全纯映照的偏差定理,得到延拓算子在Ω_N上保持强α次殆β型螺形映照、α次殆β型螺形映照和α次β型螺形映照的性质,进而得到B~n上相应的结论.所得结论包含已有的结果并为研究C~n中的双全纯映照提供了新的途径.     

On a general class of multi-valued weakly Picard mappings

The concept of weak contraction from the case of single-valued mappings is extended to multi-valued mappings and then corresponding convergence theorems for the Picard iteration associated to a multi-valued weak contraction are obtained. The main results in this paper extend, improve and unify a multitude of classical results in the fixed point theory of single and multi-valued contractive mappings and also improve recent results from the paper [P.Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl. 192 (1995), 655-666].     

Asymptotic behavior of alternative Jensen and Jensen type functional equations

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982-2005 we established the Hyers-Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002-2005 the authors of this paper investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve our bounds and thus our results obtained, in 2003 for Jensen type mappings and establish new theorems about the Ulam stability of additive mappings of the second form on restricted domains. Besides we introduce alternative Jensen type functional equations and investigate pertinent stability results for these alternative equations. Finally, we apply our recent research results to the asymptotic behavior of functional equations of these alternative types. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.     

无限族严格渐近伪压缩映象隐迭代程序的强收敛定理

在Banach空间框架下,对无限族的严格渐近伪压缩映象和无限族的非扩张映象引入了一类新的隐迭代程序,并在适当的条件下,证明了该迭代程序强收敛于这两族映象的公共不动点.结果是新的,它推广和改进了一些人的最新结果.     

On the Ulam stability of mixed type mappings on restricted domains

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982-1998 we established the Hyers-Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1983 F. Skof was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 S.M. Jung investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by S.M. Jung, in 1998. Besides we establish the Ulam stability of mixed type mappings on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types.     

The estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation in several complex variables

In this paper, we obtain the estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation on the unit ball of complex Banach spaces.Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in C~n. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.     

α次殆β型螺形映照齐次展开式的精细估计

从Loewner链的角度讨论C~n中单位球B~n上α次殆β型螺形映照齐次展开式的相关项的上界,并作为特殊情况得出β型螺形映照、星形映照和α次殆星形映照齐次展开式的相关项的上界估计,推广了螺形映照及星形映照齐次展开式的二次项系数的上界估计.     

Convergence theorems for a countable family of Lipschitzian mappings

This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We introduce a new condition for a class of mappings to obtain several weak and strong convergence theorems. This new condition is implied by many previous known conditions introduced by many authors. We also apply our results for a class of nonexpansive mappings and asymptotically nonexpansive mappings and we immediately obtain convergence theorems proved by Song-Chen, Kimura-Takahashi, Tan-Xu, and many others.     

Semicontinuity of Solution Mappings to Parametric Generalized Vector Equilibrium Problems

In this article, stability results concerning the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mappings to parametric generalized vector equilibrium problems with neither the monotonicity of mappings nor any information of the solution mappings are established by using scalarization methods and a new density result.     

A new class of contractive mappings

We introduce a new class of Picard operators which includes the class of enriched contractions, enriched Kannan mappings, enriched Chatterjea mappings, and prove some fixed point theorems for these mappings. Some examples will illustrate the generality of our results.

     

Fixed Point Theorems for Monotone Caristi Inward Mappings

In this paper, we introduce the monotone Caristi inward mappings. As an example, we show that monotone inward contraction mappings are monotone Caristi inward mappings. A general fixed point theorem for such mappings is given. A mutlivalued version of these results is also introduced.     

On the Refined Esitmates of All Homogeneous Expansions for a Subclass of Biholomorphic Starlike Mappings in Several Complex Variables

The refined estimates of all homogeneous expansions for a subclass of biholomorphic starlike mappings are mainly established on the unit ball in complex Banach spaces or the unit polydisk in Cn with a unified method. Especially the results are sharp if the above mappings are further k-fold symmetric starlike mappings or k-fold symmetric starlike mappings of order α. The obtained results unify and generalize the corresponding results in some prior literatures.     

关于1-序列商映射

引进了1-序列商映射，证明了1-序列商映射象保持sm-第一可数空间．作为这一结果的一个应用，本文证明了几乎开，闭映射保持度量空间，g-度量空间，sm-度量空间．此外本文还证明了度量空间上的1-序列商，紧映射是1-序列覆盖映射．这些结果改进并推广了广义度量空间映射象的有关理论．     

New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators

The purpose of this article is to prove the strong convergence theorems for hemi-relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems for hemi-relatively nonexpansive mappings, a new monotone hybrid iteration algorithm is presented and is used to approximate the fixed point of hemi-relatively nonexpansive mappings. Noting that, the general hybrid iteration algorithm can be used for relatively nonexpansive mappings but it can not be used for hemi-relatively nonexpansive mappings. However, this new monotone hybrid algorithm can be used for hemi-relatively nonexpansive mappings. In addition, a new method of proof has been used in this article. That is, by using this new monotone hybrid algorithm, we firstly claim that, the iterative sequence is a Cauchy sequence. The results of this paper modify and improve the results of Matsushita and Takahashi, and some others.