Fixed Point Theorem for Ɓ-type Contraction in Partial Metric Spaces

Authors

  • Bijender Singh Guru Jambheshwar University of Science and Technology, Haryana.
  • Vizender Sihag Guru Jambheshwar University of Science and Technology, Haryana.
  • Anil Ahlawat Guru Jambheshwar University of Science and Technology, Haryana.

DOI:

https://doi.org/10.12723/mjs.60.3

Keywords:

B-contraction, Contraction mappings, fixed point, common fixed point, complete metric space

Abstract

The objective of this work is to study Ɓ-types of contraction mappings in the settings of partial metric space and establish fixed point results. As a result, a fixed point theorem has been established for a pair of Ɓ-type contraction mappings with a unique common fixed point. The study's main findings, in particular, expand and extend a fixed point theorem first proposed by Bijender et. al. in 2021.

Author Biographies

Bijender Singh, Guru Jambheshwar University of Science and Technology, Haryana.

Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, Haryana, India.

Vizender Sihag, Guru Jambheshwar University of Science and Technology, Haryana.

Directorate of Distance Education, Guru Jambheshwar University of Science and Technology, Hisar, Haryana, India.

Anil Ahlawat, Guru Jambheshwar University of Science and Technology, Haryana.

Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, Haryana, India.

References

L.B.Ciric: A generalization of Banach’s contraction principle, Proceedings of the American Mathematical Society, vol. 45, 267-273(1974).

S. G. Matthews: Partial metric topology, Annals of the New York Academy of Sciences, Proc. 8th Summer Conference on General Topology and Applications, vol. 728, 183-197(1994).

L. Ciric, B. Samet, H. Aydi, and C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Applied Mathematics and Computation, vol. 218, no. 6, 2398-2406(2011).

D. Wardowski, Fixed Points of a new type of Contractive mappings in Complete Metric Spaces, Fixed Point Theory and Application, 94(2012).

B.Singh, V. Singh, Fixed Point Theorems for New Type of Mappings in Metric Spaces and Application, Journal of International Academy of Physical Sciences, 25(1), 11-24(2021).

M. Bukatin, R.Kopperman, S. Matthews, Partial metric spaces, Am. Math.Mon, 116, 708-718(2009).

Additional Files

Published

2022-01-01