An order theoretic approach in fixed point theory

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• 作者：Yaé Ulrich Gaba
• 关键词：Quasi ; pseudometric space ; Left $$K$$ K ; complete ; Preordered space ; Weakly left ; related ; 47H10 ; 47H03
• 刊名：Mathematical Sciences
• 出版年：2014
• 出版时间：November 2014
• 年：2014
• 卷：8
• 期：3
• 页码：87-93
• 全文大小：216 KB
• 参考文献：1. Agarwal, RP, El-Gebeily, MA, O’Regan, D (2008) Generalized contractions in partially ordered metric spaces. Appl. Anal. 87: pp. 1-8 CrossRef
  2. Lakshmikantham, V, Ciric, LjB (2009) Coupled fixed point theorems for nonlinear contractions in partially ordered metric space. Nonlinear Anal. 70: pp. 4341-4349 CrossRef
  3. Mustafa, Z., Sims, B.: Fixed point theorems for contractive mapping in complete G-metric spaces. Fixed Point Theory Appl. (2009). doi:10.1155/2009/917175
  4. Bhaskar, TG, Lakshmikantham, V (2006) Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65: pp. 1379-1393 CrossRef
  5. W?odarczyk, K, Plebaniak, R (2013) Asymmetric structures, discontinuous contractions and iterative approximation of fixed and periodic points. Fixed Point Theory Appl. 128: pp. 1-18
  6. Gaba, Y.U.: Startpoints and \((\alpha ,\gamma )\) -contractions in quasi-pseudometric spaces. J. Math. (2014). doi:10.1155/2014/709253 (Article ID 709253, 8 pages)
  
• 刊物主题：Applications of Mathematics;
• 出版者：Springer Berlin Heidelberg
• ISSN：2251-7456

文摘

In the present article, we show the existence of a coupled fixed point for an order preserving mapping in a preordered left \(K\) -complete quasi-pseudometric space using a preorder induced by an appropriate function. We also define the concept of left-weakly related mappings on a preordered space and discuss common coupled fixed points for two and three left-weakly related mappings in the same space. Similar results are given for right-weakly related mappings, the dual notion of left-weakly related mappings.