Fixed point theorems of ordered contractive mappings on cone metric spaces over Banach algebras

详细信息    查看全文

• 作者：Jiandong Yin (1)
  Tao Wang (1)
  Qi Yan (1)
  
  1. Department of Mathematics ; Nanchang University ; Nanchang ; 330031 ; China
  
• 关键词：54H25 ; 47H10 ; fixed point theorems ; ordered contractive mappings ; cone metric spaces over Banach algebras ; spectral radius
• 刊名：Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,219 KB
• 参考文献：1. Guo, D-J, Lakshmikantham, V (1987) Coupled fixed point of nonlinear mappings with applications. Nonlinear Anal. 11: pp. 623-632 CrossRef
  2. Guo, D-J, Lakshmikantham, V (1988) Nonlinear Problems in Abstract Cone. Academic Press, New York
  3. Sun, Y (1991) A fixed point theorem for mixed monotone mappings with applications. J. Math. Anal. Appl. 156: pp. 240-246 CrossRef
  4. Guo, D-J (1992) Existence and uniqueness of positive fixed point for mixed monotone mappings and applications. Appl. Anal. 46: pp. 91-100 CrossRef
  5. Rhoades, B-E (2001) Some theorems on weakly contractive maps. Nonlinear Anal. 47: pp. 2683-2693 CrossRef
  6. Caristi, J (1976) Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215: pp. 241-251 CrossRef
  7. Huang, L-G, Zhang, X (2007) Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332: pp. 1468-1476 CrossRef
  8. Rezapour, S, Hamlbarani, R (2008) Some notes on the paper 鈥楥one metric spaces and fixed point theorems of contractive mappings鈥? J. Math. Anal. Appl. 345: pp. 719-724 CrossRef
  9. Ili膰, D, Rako膷evi膰, V (2009) Quasi-contraction on a cone metric space. Appl. Math. Lett. 22: pp. 728-731 CrossRef
  10. Radenovi膰, S, Rhoades, B-E (2009) Fixed point theorems for two non-self mappings in cone metric spaces. Comput. Math. Appl. 57: pp. 1701-1707 CrossRef
  11. Jankovi膰, S, Kadelburg, Z, Radenovi膰, S (2011) On the cone metric space: a survey. Nonlinear Anal. 74: pp. 2591-2601 CrossRef
  12. Gaji膰, L, Rako膷evi膰, V (2012) Quasi-contractions on a nonnormal cone metric space. Funct. Anal. Appl. 46: pp. 75-79
  13. Du, W-S (2010) A note on cone metric fixed point theory and its equivalence. Nonlinear Anal. 72: pp. 2259-2261 CrossRef
  14. Kadelburg, Z, Radenovi膰, S, Rako膷evi膰, V (2011) A note on the equivalence of some metric and cone metric fixed point results. Appl. Math. Lett. 24: pp. 370-374 CrossRef
  15. Huang, H-P, Xu, S-Y, Liu, H, Radenovi膰, S: Fixed point theorem and / T stability of Picard iteration for generalized Lipschitz mappings in cone metric spaces over Banach algebra. J. Comput. Anal. Appl. (to appear)
  16. Huang, H-P, Radenovi膰, S: Some fixed point results of generalized Lipschitz mappings on cone / b-metric spaces over Banach algebras. J. Comput. Anal. Appl. (to appear)
  17. Kadelburg, Z, Radenovi膰, S, Rak菕cev铆c, V (2010) Topological vector space-valued cone metric spaces and fixed point theorems. Fixed Point Theory Appl. 2010: CrossRef
  18. Ding, H-S, Kadelburg, Z, Karapinar, E, Radenovi膰, S (2012) Common fixed points of weak contractions in cone metric spaces. Abstr. Appl. Anal. 2012:
  19. Rahimi, H, Radenovi膰, S, Soleimani, G-R, Kumam, P (2014) Quadrupled fixed point results in abstract metric spaces. Comput. Appl. Math..
  20. Kadelburg, Z, Radenovi膰, S (2012) Generalized quasicontractions in orbitally complete abstract metric spaces. Fixed Point Theory 13: pp. 527-536
  21. Ghafur, AB, Fadail, ZM, Abbas, M, Kadelburg, Z, Radenovi膰, S (2012) Some fixed points in abstract metric spaces. Abstr. Appl. Anal. 2012:
  22. Radenovi膰, S, Kadelburg, Z (2011) Quasi-contractions on symmetric and cone symmetric spaces. Banach J. Math. Anal. 5: pp. 38-50 CrossRef
  23. Kadelburg, Z, Radenovi膰, S (2013) A note on various types of cones and fixed point results in cone metric spaces. Asian J. Math. Appl. 2013:
  24. Liu, H, Xu, S-Y (2013) Fixed point theorem of quasi-contractions on cone metric spaces with Banach algebras. Abstr. Appl. Anal. 2013:
  25. Liu, H, Xu, S-Y (2013) Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings. Fixed Point Theory Appl. 2013: CrossRef
  26. Xu, S-Y, Radenovi膰, S (2014) Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality. Fixed Point Theory Appl. 2014: CrossRef
  
• 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 paper, the concept of ordered contractive mappings is introduced on cone metric spaces over Banach algebras, and some existence theorems of fixed points for such mappings are obtained. As an application of a result, an example is given at the end of the paper.