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The Journal of Analysis

, Volume 27, Issue 1, pp 121–136 | Cite as

Contraction mapping in hexagonal cone b-metric spaces over Banach algebras and related fixed point theorems

  • G. KalpanaEmail author
  • Z. Sumaiya Tasneem
Original Research Paper
  • 43 Downloads

Abstract

In this paper, we introduce the concept of hexagonal cone b-metric spaces over Banach algebras as a generalization of cone hexagonal metric spaces and cone b-hexagonal metric spaces. An example is given at the end of the paper to show the applicability and validity of our results.

Keywords

Hexagonal cone b-metric spaces over Banach algebras c-sequence Contraction mapping Fixed points 

Mathematics Subject Classification

47H10 54H25 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human/animals participants

The authors declare that there is no research involving human participants and/or animals in the contained of this paper.

References

  1. 1.
    Auwalu, A., and Ali Denker. 2017. Contraction mapping in cone b-hexagonal metric spaces. Global Journal of Pure and Applied Mathematics 13 (6): 1651–1662.Google Scholar
  2. 2.
    Auwalu, A., and E. Hincal. 2016. A note on Banach contraction mapping principle in cone hexagonal metric space. British Journal of Mathematics & Computer Science 16 (1): 1–12.CrossRefzbMATHGoogle Scholar
  3. 3.
    Auwalu. A. 2018. Pentagonal cone b-metric spaces over Banach algebras and fixed point theorems of generalized Lipschitz mappings. In 3rd International Conference on Computational Mathematics and Engineering Sciences Held at Final International University, Girne, North Cyprus.Google Scholar
  4. 4.
    Auwalu, A., and E. Hincal. 2016. The Kannan’s fixed point theorem in a cone hexagonal metric spaces. Advances in Research 7 (1): 1–9.CrossRefzbMATHGoogle Scholar
  5. 5.
    Bai, Chuanzhi. 2016. Common fixed point theorems for generalized ordered contractive mappings on cone b-metric spaces over Banach algebras. Journal of Nonlinear Sciences & Applications 9: 5766–5771.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 7.
    Garg, M. 2014. Banach contraction principle on cone hexagonal metric space. Ultra Scientist 26 (1): 97–103.zbMATHGoogle Scholar
  7. 8.
    George, R., Hossam A. Nabwey, R. Rajagopalan, Stojan Radenvić, and K.P. Reshma. 2017. Rectangular cone b-metric spaces over Banach algebras and contraction principle. Fixed Point Theory and Applications 2017: 14.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 9.
    Huang, H., and S. Radenovic. 2015. Common fixed point theorem of generalised Lipschitz mappings in cone b-metric spaces over Banach algebras and applications. Journal of Nonlinear Science 8: 787–799.CrossRefzbMATHGoogle Scholar
  9. 10.
    Hussain, N., and M.H. Shah. 2011. KKM mapping in cone b-metric spaces. Computers and Mathematics with Applications 62 (4): 1677–1684.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 11.
    Long-Guang, Huang, and Zhang Xian. 2007. Cone metric spaces and fixed point theorems of contractive mappings. Journal of Mathematical Analysis and Applications 332 (2): 1468–1476.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 12.
    Liu, H., and S. Xu. 2013. Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings. Fixed Point Theory Appl 2013: 320.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 13.
    Rudin, W. 1991. Functional Analysis, 2nd ed. New York: McGraw-Hill.zbMATHGoogle Scholar
  13. 14.
    Xu, S., and S. Radenovic. 2014. Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality. Fixed Point Theory Appl 2014: 102.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsSSN College of EngineeringChennaiIndia

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