Unification of several distance functions and a common fixed point result

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• 作者：Mujahid Abbas ; Bashir Ali ; Yusuf I Suleiman
• 关键词：47H10 ; 47H09 ; 54H25 ; dislocated ; quasi ; metric spaces ; A ; metric spaces ; coincidence points ; fixed points ; weakly compatible mappings
• 刊名：Fixed Point Theory and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,423 KB
• 参考文献：1. Scott, DS: Domains for Denotational Semantics. Lecture Notes in Computer Science, vol. 140 (1982)
  2. Matthews, SG: Partial metric topology. In: Proceedings of the 8th Summer Conference on General Topology and Applications, Flushing, NY, 1992. Annals of the New York Academy of Sciences, vol. 728, pp. 183-197. N.Y. Acad. Sci., New York (1994)
  3. Arshad, M, Shoaib, A, Beg, I: Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space. Fixed Point Theory Appl. 2013, Article ID 115 (2013) MathSciNet CrossRef
  4. Abbas, M, Ali, B, Suleiman, YI: Generalized common fixed point results in partially ordered A-metric spaces. Fixed Point Theory Appl. 2015, Article ID 84 (2015) MathSciNet CrossRef
  5. Hussain, N, Roshan, JR, Parvaneh, V, Latif, A: A unification of G-metric, partial metric, and b-metric spaces. Abstr. Appl. Anal. 2014, Article ID 180698 (2014). doi:10.​1155/​2014/​180698 MathSciNet
  
• 作者单位：Mujahid Abbas (1)
  Bashir Ali (2)
  Yusuf I Suleiman (3)
  
  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield, Pretoria, South Africa
  2. Department of Mathematics, Bayero University Kano, P.M.B. 3011, Kano, Nigeria
  3. Department of Mathematics, Kano University of Science and Technology, P.M.B. 3042, Wudil, Kano, Nigeria
  
• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

In this work, we initiate the notions of dislocated-\(A_{b}\)-quasi-metric and \(A_{b}\)-quasi-metric-like spaces. Then we establish the existence of a common fixed point of weakly compatible mappings satisfying a contractive condition on a closed neighborhood of dislocated \(A_{b}\)-quasi-metric spaces. Some examples are given to show that these spaces are more general than various known comparable metric spaces. Our result unify, complement, and generalize various known results in the literature. Keywords dislocated-quasi-metric spaces A-metric spaces coincidence points fixed points weakly compatible mappings