Fixed and common fixed point theorems in frame of quasi metric spaces under contraction condition based on ultra distance functions

In this paper, we introduce the notion of ultra distance function. Based on the notion of ultra distance function, we introduce the definitions of (k, ψ, L)-quasi contractions of type (I) and type (II) in the frame of quasi metric spaces. We employ our new definitions to construct and prove many fix...

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Bibliographic Details
Published inNonlinear analysis (Vilnius, Lithuania) Vol. 23; no. 5; pp. 724 - 748
Main Author Shatanawi, Wasfi
Format Journal Article
LanguageEnglish
Published Vilnius University Press 01.01.2018
Subjects
almost perfect mappings
comparison functions
fixed-point theorems
nonlinear contractions
quasi metric spaces
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Summary:In this paper, we introduce the notion of ultra distance function. Based on the notion of ultra distance function, we introduce the definitions of (k, ψ, L)-quasi contractions of type (I) and type (II) in the frame of quasi metric spaces. We employ our new definitions to construct and prove many fixed and common fixed point results in the frame of quasi metric spaces. Our results extend and improve many exciting results in the literatures. Also, we introduce some examples and some applications in order to support the usability of our work.
ISSN:1392-5113
2335-8963
DOI:10.15388/NA.2018.5.6