Banach contraction principle for cyclical mappings on partial metric spaces

Fixexd point theory and applications

A Mukheimer¹  Y Zaidan¹  T Abdeljawad²  JO Alzabut³ 

[1] Department of Mathematics and Physical Sciences, Prince Sultan University, Riyadh, Saudi Arabia;Department of Mathematics, Çankaya University, Ankara, Turkey

关键词: partial metric space;    fixed point;    cyclic mapping;    Banach contraction principle;    0-compact set;   

DOI  :  10.1186/1687-1812-2012-154

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilić et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact. MSC:47H10, 54H25.

【 授权许可】

CC BY