新型Ciric类F-压缩映射不动点定理  

A fixed point theorem for new Ciric type F-contraction mappings

作　　者：沈洁[1] 陈颖[1] 金希[1] 赵睿[1] 高亚丽[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2016年第1期7-10,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11301246)

摘　　要：不动点相关理论作为数学科学中的主流工具,是研究各类非线性问题的一个不可或缺的工具.近年来,它成为许多专家学者研究的热点,这就使得不动点理论有了很大的发展,许多重要的数学成果都是借助于它获得的.在非线性泛函分析、数学分析、拓扑学等众多领域中都可以见到它的应用.在完备度量空间中研究了一类新型的单值映射,对Ozlem等人给出的Ciric类型广义F-压缩进行了拓展,在原有概念的基础上引入了映射g,并定义了一种新的关于g的F-压缩映射,同时,借助于广义比较函数,深入研究了新型映射不动点的存在性问题,最后得出在一定条件下T,g存在不动点的结论.As a main tool of mathematical science,fixed point theory occupies a very important position in the study of various nonlinear problems.In recent years,fixed point theory has become a study hotspot for many experts and scholars,which promotes its rapid development,hence many important mathematical results are obtained.This theory is applied in widespread fields,such as nonlinear functional analysis,mathematical analysis,general topology,etc.This paper studies a new kind of single-valued mappings in a complete metric space and further extends Ciric type generalized F-contraction proposed by Ozlem,et al.Based on the original concept,the mapping g is introduced.We define a new F-contraction mapping with respect to g.The existence of fixed points is discussed with the help of generalized comparison function.Under certain conditions,the existence of fixed points of gcan be assured.

关 键 词：不动点 F-压缩映射 完备度量空间 广义比较函数 

分 类 号：O177.91[理学—数学]