Fixed point results for cyclic contractions in Menger PM-spaces and generalized Menger PM-spaces

被引：11
作者：
Wu, Zhaoqi [1 ,2 ]
Zhu, Chuanxi [1 ,2 ]
Yuan, Chenggui [3 ]
机构：
[1] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China
[2] Nanchang Univ, Sch Sci, Numer Simulat & High Performance Comp Lab, Nanchang 330031, Jiangxi, Peoples R China
[3] Swansea Univ, Dept Math, Singleton Pk, Swansea SA2 8PP, W Glam, Wales
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2018年 / 112卷 / 02期
关键词：
Menger PM-space; Generalized Menger PM-space; Fixed point; Cyclic phi-contraction; Cyclic weak phi-contraction; METRIC-SPACES; PHI-CONTRACTIONS; MAPPINGS; THEOREMS;
D O I：
10.1007/s13398-017-0393-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce the concepts of cyclic -contractions in Menger PM-spaces and cyclic weak phi-contractions in generalized Menger PM-spaces. Based on these concepts, some fixed point results for cyclic phi-contractions in Menger PM-spaces are obtained. Furthermore, some fixed point theorems for cyclic weak phi-contractions and cyclic -contractions in generalized Menger PM-spaces are obtained by assuming that the number of cyclic sets is odd. An example is also given to show the validity of our main results.
引用
收藏
页码：449 / 462
页数：14
相关论文
共 23 条
[1]  
[Anonymous], 2011, Probabilistic Metric Spaces
[2]  
Branciari A, 2000, PUBL MATH-DEBRECEN, V57, P31
[3]  
Chang S-S, 2001, NONLINEAR OPERATOR T
[4]  
Hadzic O., 2001, Fixed Point Theory in Probabilistic Metric Spaces, Mathematics and Its Applications
[5]  
He F., 2016, FIXED POINT THEORY A, V2016, P67
[6]   Fixed point theory for cyclic weak φ-contraction (vol 24, pg 822, 2011) [J].
Karapinar, Erdal ;
Sadarangani, Kishin .
APPLIED MATHEMATICS LETTERS, 2012, 25 (10) :1582-1584
[7]   Fixed point theory for cyclic weak φ-contraction [J].
Karapinar, Erdal .
APPLIED MATHEMATICS LETTERS, 2011, 24 (06) :822-825
[8]  
Kirk A., 2003, Fixed Point Theory, V4, P79
[9]   Generalized metrics and Caristi's theorem [J].
Kirk, William A. ;
Shahzad, Naseer .
FIXED POINT THEORY AND APPLICATIONS, 2013,
[10]   Common fixed points for α-ψ-φ-contractions in generalized metric spaces [J].
La Rosa, Vincenzo ;
Vetro, Pasquale .
NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2014, 19 (01) :43-54
123