Title: Fixed Points of α-Admissible Mappings in Cone Metric Spaces with Banach Algebra
Author(s): S.K. Malhotra, J.B. Sharma, Satish Shukla
Pages: 9-18
Cite as:
S.K. Malhotra, J.B. Sharma, Satish Shukla, Fixed Points of α-Admissible Mappings in Cone Metric Spaces with Banach Algebra, Int. J. Anal. Appl., 9 (1) (2015), 9-18.

Abstract


In this paper, we introduce the $\alpha$-admissible mappings in the setting of cone metric spaces equipped with Banach algebra and solid cones. Our results generalize and extend several known results of metric and cone metric spaces. An example is presented which illustrates and shows the significance of results proved herein.

Full Text: PDF

 

References


  1. A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2003) 1435-1443. Google Scholar

  2. B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis, 75 (2012) 2154-2165. Google Scholar

  3. H. C¸ akallı, A. S¨onmez, C¸. Gen¸c, On an equivalence of topological vector space valued cone metric spaces and metric spaces, Appl. Math. Lett., 25, (2012) 429-433. Google Scholar

  4. H. Liu and S.-Y. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl., 2013, 2013:320. Google Scholar

  5. H. Liu and S.-Y. Xu, Fixed point theorems of quasi-contractions on cone metric spaces with Banach algebras, Abstarct and Applied Analysis, Volume 2013, Article ID 187348, 5 pages. Google Scholar

  6. J.J. Nieto, R. Rodr´ıguez-L´opez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239. Google Scholar

  7. L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007) 1468-1476. Google Scholar

  8. S. Radenovi´c, B.E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces, Comput. Math. Appl., 57, 1701-1707 (2009) Google Scholar

  9. S. Xu, S. Radenovi´c, Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality, Fixed Point Theory Appl., 2014, 2014:102. Google Scholar

  10. Sh. Rezapour and R. Hamlbarani, Some notes on the paper Cone metric spaces and fixed point theorems of contractive mappings, Math. Anal. Appl., 345 (2008), 719-724. Google Scholar

  11. W. Rudin, Functional Analysis, 2nd ed., McGraw-Hill, 1991. Google Scholar

  12. W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4(1)(2003), 79-89. Google Scholar

  13. W.S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72(5), (2010) 2259-2261. Google Scholar

  14. Y. Feng, W. Mao, The equivalence of cone metric spaces and metric spaces, Fixed Point Theory, 11(2), (2010) 259-264. Google Scholar

  15. Z. Kadelburg, M. Pavlovi´c, S. Radenovi´c, Common fixed point theorems for ordered contractions and quasi-contractions in ordered cone metric spaces, Comput. Math. Appl. 59, 3148-3159 (2010) Google Scholar

  16. Z. Kadelburg, S. Radenovi´c, V. Rakoˇcevi´c, A note on the equivalence of some metric and cone metric fixed point results, Appl. Math. Lett., 24, (2011) 370-374. Google Scholar


COPYRIGHT INFORMATION

Copyright © 2020 IJAA, unless otherwise stated.