b-度量空间中一类积分型压缩映射的公共不动点定理  

Common fixed point theorems for a class of contractive mappings of integral type in b-metric spaces

作　　者：关洪岩[1] 勾金泽 GUAN Hongyan;GOU Jinze(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2023年第6期562-567,共6页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅基本科研项目(JYTMS20231700)。

摘　　要：不动点理论是非线性泛函分析的重要组成部分,在处理许多非线性问题时起着十分关键的作用。Banach压缩映像原理是不动点理论研究中的热点问题之一,近年来经过学者们的深入研究,该定理在许多方面得到了拓展,取得了大量优秀的成果。在b-度量空间的框架下,首次考虑了积分型压缩映射的不动点问题。首先,在该类空间中提出了一类新的积分型压缩的概念,并根据映射对的包含关系构造出一个序列,再利用反证法和压缩条件证明了此序列是该空间中的一个柯西列;其次,通过该空间的完备性和映射对的弱相容性,证明了该空间中积分型压缩映射对的公共不动点的存在性及唯一性;最后,给出一个具体例子说明了该结果的有效性。Fixed point theory is an important part of nonlinear functional analysis and plays a key role,while Banach contraction mapping principle is one of the hot issues in the research of fixed point theory.In recent years,through continuous in-depth research by scholars,this result has been expanded in different aspects and has achieved many excellent results.In the framework of b-metric spaces,a fixed point problem of contractive mapping of integral type is considered for the first time.First,we introduce a new class of contractive mapping of integral type.Second,we construct a sequence according to the inclusion relation of the mappings and prove that the sequence is Cauchy by the mathematical induction and the contraction conditions.The existence and uniqueness of the common fixed point of a pair of the contractive mappings of integral type are proved by the completeness of the space and the weak compatibility of the mappings in this space.Finally,a concrete example is given to prove the validity of the result.

关 键 词：不动点 b-度量空间 压缩映射 积分型 柯西列 

分 类 号：O177.91[理学—数学]