Some fixed point theorems on b-metric spaces ∗

Authors

  • Jayesh Tiwari Department of Computer Science, Shri Vaishnav Institute of Management, Devi Ahilya University, Indore, Madhya Pradesh-452009, India.
  • Dileep Kumar Sharma Department of Mathematics, Government Polytechnic College, Barwani, Madhya Pradesh-451551, India.
  • Koti NVV Vara Prasad Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgarh-495009, India.

DOI:

https://doi.org/10.48165/

Keywords:

b-metric space, b-metric space, fixed point, fixed point, contraction mappings, contraction mappings

Abstract

 In this paper, we introduce new contractive mappings in the setup of com pleteness and uniqueness of fixed point theorem on b-metric space. We improve the recent fixed point results established by Agrawal et al. (Agrawal, S., Qureshi, K. and Nema, J., A fixed point theorems for b-metric space, IJPAM, 9(1), 2016, 45–50). We also show that different contractive type mappings exist in b-metric space. 

References

Agrawal, S., Qureshi, K. and Nema, J. (2016). A fixed point theorems for b-metric space, Inter national Journal of Pure and Applied Mathematical Sciences, 9(1), 45–50.

Aydi, H., Bota M.F., Karasinar, E. and Moradi, S. (2012). A common fixed point for weak ϕ contractions on b-metric spaces, Fixed Point Theory, 13(1), 337–346.

Bakhtin, I.A. (1989). The contraction mapping principle in almost metric spaces, Functional Anal ysis, Unianowsk Gos. Ped. Inst., 30(30), 26–37.

Banach, S. (1922). Surles operations dans les ensembles abstract et leur application aux equation integrals, Fund. Math., 3(1), 133–181.

Bota, M., Molnar, V. and Csaba, Varga (2011). On Ekeland variational principle in b-metric spaces, Fixed Point Theory, 12(2), 21–28.

Boriceanu, M. (2009). Strict fixed point theorems for multivalued operators in b-metric spaces, Inter. J. Mod. Math., 4(2), 285–301.

Boriceanu, M., Bota, M. and Petrusel, Adrian (2010). Multivalued fractals in b-metric spaces, Cen. Eur. J. Math., 8(2), 367–377.

Czerwik, S. (1993). Contraction mappings in b-metric spaces, Acta. Math. Inform. Univ. Os traviensis, 1(1), 5–11.

Czerwik, S. (1988). Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semi. Mat. Univ. Modena, 46(2), 263–276.

Published

2021-06-30

How to Cite

Tiwari, J., Sharma, D.K., & Prasad, K.N.V. (2021). Some fixed point theorems on b-metric spaces ∗ . Bulletin of Pure & Applied Sciences- Mathematics and Statistics, 40(1), 18–25. https://doi.org/10.48165/