积分型F-压缩映射的公共不动点定理  

A common fixed point theorem of integral type F-contractive mappings

作　　者：张向帅 ZHANG Xiangshuai(College of Mathematical Sciences,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《渤海大学学报（自然科学版）》2022年第3期246-252,共7页Journal of Bohai University:Natural Science Edition

摘　　要：主要借鉴Branciari和Phaneendra等人的思想,在G-度量空间中对Banach压缩映射原理进行探索,给出了一个积分型F-压缩映射的公共不动点定理.共分为三个部分:第一部分是引言和研究背景,着重阐述国内外学者对G-度量空间中单值积分型压缩映射、度量空间中单值F-压缩映射所进行的研究工作及其获得的某些结果;第二部分是预备知识,主要介绍文中涉及到的一些定义、符号、基础知识和引理;第三部分是主体,主要以Branciari, Wardowski和Aydi等人的成果为基础,结合Shoaib等人的创新想法,在G-度量空间中给出了一个单值积分型F-压缩映射的公共不动点定理.该定理不同于前人已取得的成果,并推广了文献[8]中的定理3.5.The paper is chiefly employed the thought of which Branciari and Phaneendra explored Banach contraction principle, giving a common fixed point theorem of integral type F-contractive mappings in G-metric spaces.The paper consists of three parts.The first part is composed of introduction and backgrounds.It mainly recommends the works and conclusions of single-valued contractive mappings of integral type in G-metric spaces and single-valued F-contractive mappings in metric spaces which the domestic and foreign researchers carried out.The second part is preliminaries, it mainly introduces the definitions, symbols, fundamental knowledge and lemmas used in the paper.The third part is the core of this paper, on the basis of Branciari, Wardowski and Aydi’s results and with the help of the innovative ideas of Shoaib, a common fixed point theorem of integral type F-contractive mappings in G-metric is provided.The theorem is different from results which predecessors obtained, and generalizes the theorem 3.5 in references[8].

关 键 词：G-度量空间 单值积分型F-压缩映射 公共不动点定理 

分 类 号：O177.91[理学—数学]