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首页> 外文期刊>Fixexd point theory and applications >Weak and strong convergence theorems of fixed points for nonexpansive mappings and strongly pseudocontractive mappings in a new class of probabilistic normed spaces
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Weak and strong convergence theorems of fixed points for nonexpansive mappings and strongly pseudocontractive mappings in a new class of probabilistic normed spaces

机译：一类新的概率赋范空间中非膨胀映象和强伪压缩映象的不动点的弱和强收敛定理

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摘要

The purpose of this paper is to present a new class of probabilistic normed spaces and to study fixed point problems in this class of probabilistic normed spaces. This paper includes the following two contents: (1) The definition of a new class of probabilistic normed spaces, the so-called S-probabilistic normed spaces, is given. In order to study the fixed point problems, some relevant properties of S-probabilistic normed spaces are discussed and some basic useful results are obtained; (2) The notion of probabilistic weak convergence is firstly presented in this paper. Therefore the probabilistic weak and strong convergence theorems of fixed points for nonexpansive mappings, asymptotically nonexpansive mappings and strongly pseudocontractive mappings are also proved by using the new methods and techniques.
机译：本文的目的是提出一种新的概率范数空间，并研究此类概率范数空间中的不动点问题。本文包括以下两个内容：（1）给出了新一类概率范数空间的定义，即所谓的S-概率范数空间。为了研究不动点问题，讨论了S概率赋范空间的一些相关性质，并获得了一些基本的有用结果。 （2）本文首先提出了概率弱收敛的概念。因此，还使用新方法和新技术证明了非扩张映射，渐近非扩张映射和强伪压缩映射的不动点的概率弱弱和强收敛定理。

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