复一致凸和复一致平滑Banach空间的几点注记

Ｖ．Ｉ．Ｉｓｔｒａｔｅｓｃｕ引入了复一致凸性和复一致平滑性的概念．本文证明了它们分别等价于一致凸性和一致平滑性．

一致平滑Banach空间的特征

<正> Hilbert空间内积公式||x+y||~2=||x||~2+2<x,y>+||y||~2的变形推广,在应用上具有重要意义,本文后一作者对其作了详细的研究。

p－一致平滑空间局部Lipschitz方程解的迭代逼近

设Ｘ为ｐ－一致平滑的Ｂａｎａｃｈ空间，ｐ∈［１，２］，Ｔ：Ｄ（Ｔ）→Ｘ是局部Ｌｉｐｓｃｈｉｔｚ和严格增殖算子，本文给出了非线性方程ＴＸ＝Ｙ的解的迭代逼近，所得结果推广了文［１］的主要结果。

一致平滑可分的Banach空间中K-正定算子方程的逼近解(英文)

设Ｅ是可分的一致平滑Ｂａｎａｃｈ空间，Ａ：Ｄ（Ａ）Ｅ→Ｅ是一个Ｋ－正定算子。构造了一个迭代序列强收敛于算子方程Ａｘ＝ｆ（ｆ∈Ｅ）的唯一解。所做工作推广了Ｃｈｉｄｕｍｅ与Ｏｓｉｌｉｋｅ，Ｃｈｉｄｕｍｅ与Ａｎｅｋｅ等人的结果。

巴拿赫空间中两类压缩映射的不动点迭代法

该文讨论了两类压缩映象的不动点迭代问题,一类是李普希茨强增生映象,一类是所谓的拟压缩映象,并分别讨论了Mann迭代序列和Ishikawa迭代序列收敛于它的不动点问题。推广了Chidume和Tan K K的某些结果,使得这些迭代结果适用的范围更广。

Operator Equations and Duality Mappings in Sobolev Spaces with Variable Exponents

After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.