Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

被引：0

作者：

Jafari, Shahnaz ^{[1
]}

Shams, Maryam ^{[1
]}

Ibeas, Asier ^{[2
]}

De La Sen, Manuel ^{[3
]}

机构：

[1] Univ Shahrekord, Dept Pure Math, Shahrekord 8818634141, Iran

[2] UAB, Dept Telecommun & Syst Engn, Fac Engn, Barcelona 08193, Spain

[3] Univ Basque Country, Inst Res & Dev Proc IIDP, Fac Sci & Technol, POB 644, Leioa 48940, Bizkaia, Spain

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2019年 / 24卷 / 05期

关键词：

enhanced probabilistic metric space; fixed point; linear combination; convergent sequence; dynamic systems; ALTERING DISTANCES; THEOREMS; OPTIMIZATION;

D O I：

10.15388/NA.2019.5.8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the concept of enhanced probabilistic metric space (briefly EPM-space) as a type of probabilistic metric space. Also, we investigate the existence of fixed points for a (finite or infinite) linear combination of different types of contractive mappings in EPM-spaces. Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite family of contractive mappings) to a common fixed point. The useful application of this research is the study of the stability of switched dynamic systems, where we study the conditions under which the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive or not), converge to the fixed point. Also, some examples are given to support the obtained results. In the end, a number of figures give us an overview of the examples.

引用

页码：819 / 837

页数：19

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