Some remarks on mappings satisfying cyclical contractive conditions

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• 作者：Stojan Radenović
• 关键词：Cyclic type contractions ; Fixed point theorem ; Geraghty’s type theorem ; Boyd–Wong theorem ; Edelstein’s theorem ; Caristi’s type theorem ; 47H10 ; 54H25
• 刊名：Afrika Matematika
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：27
• 期：1-2
• 页码：291-295
• 全文大小：359 KB
• 参考文献：1.Banach, S.: Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fund. Math. 3, 133–181 (1922)MATH
  2.Boyd, D.W., Wong, J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–464 (1969)CrossRef MathSciNet MATH
  3.Caristi, J.: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241–251 (1976)CrossRef MathSciNet MATH
  4.Edelstein, M.: On fixed and periodic points under-contractive mappings. J. London Math. Soc. 37, 74–79 (1962)CrossRef MathSciNet MATH
  5.Geraghty, M.A.: On contractive mappings. Proc. Am. Math. Soc. 40, 604–608 (1973)CrossRef MathSciNet MATH
  6.Kirk, W.A., Srinivasan, P.S., Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4(1), 79–89 (2003)MathSciNet MATH
  
• 作者单位：Stojan Radenović (1)
  
  1. Faculty of Mathematics and Information Technology, Teacher Education, Dong Thap University, Cao Lanch, Dong Thap, Vietnam
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

In this paper, we consider, discuss and complement fixed points results for mappings satisfying cyclical contractive conditions established by Kirk et al. (Fixed Point Theory 4(1):79–89, 2003). By using our new Lemma we get much shorter and nicer proofs of some results with the new concept of mappings. Keywords Cyclic type contractions Fixed point theorem Geraghty’s type theorem Boyd–Wong theorem Edelstein’s theorem Caristi’s type theorem