Fixed Point Theorem for Fuzzy B-type Contractions in Fuzzy Metric Spaces

Authors

  • Vizender Singh Guru Jambheshwar University of Science and Technology, Haryana.
  • Bijender Singh 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.64.1

Keywords:

Fuzzy Metric Space, Fixed Point, Complete Metric Space, Fuzzy B-Contraction

Abstract

Recently, in 2021, Bijender et al. proposed the establishment of  -contraction. Such sort of contraction is a genuine generalization of the standard contraction in the study of metric fixed point theory. The aim of the present study is the establishment of the novel concept of the fuzzy B-type contraction in the settings of fuzzy metric space and such contractions are also used to establish a few fixed point theorems.

Author Biographies

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

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

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

Department of Mathematics, 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

Zadeh LA: Fuzzy sets, Inform. Control, 8, 338-353(1965).

George A and Veeramani P: On some results in fuzzy metric spaces, Fuzzy Sets and

Systems, 64, 395-399(1994).

George A and Veeramani P: On some results of analysis for fuzzy metric spaces, Fuzzy Sets

and Systems, 90, 365-399(1997).

Kramosil I and Michalek J: Fuzzy metric and statistical metric spaces, Kybernetika, 11(5),

-344(1975).

Bijender S and Vizender S: Fixed Point Theorems for New Type of Mappings in Metric

Spacecs and Application, Journal of International Academy of Physical Sciences, 25(1),

-24(2021).

Schweizer B and Sklar A: Statistical metric spaces, Pacific Journal of Mathematics, 10,

-334(1960).

Grabiec M: Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(3),

-389(1988).

Beg I, Sedghi S and Shobe N: Fixed point theorems in fuzzy metric space, International

Journal of Anaysis, (2013).

Additional Files

Published

2022-10-01