Fixed point theorems in new generalized metric spaces

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• 作者：Erdal Karapınar ; Donal O’Regan…
• 关键词：Generalized metric space ; b ; metric space ; fixed point ; contractive mapping
• 刊名：Journal of Fixed Point Theory and Applications
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：18
• 期：3
• 页码：645-671
• 全文大小：939 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-7746
• 卷排序：18

文摘

The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler–Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.