ON COMPLEX VALUED FUZZY b - METRIC SPACE
By
Gopal Yadav1, Rajesh Kumar Sharma2 and Gend Lal Prajapati3
1Department of Engineering Science & Humanities, Indore Institute of Science & Technology,
Rau-Pithampur Road, Indore, Madhya Pradesh, India-453331
2Department of Mathematics, Jawaharlal Nehru Smriti PG College, Shujalpur, Madhya Pradesh, India-465333
3Department of Computer Engineering, Institute of Engineering & Technology, Devi Ahilya University,
Khandwa Road, Indore, Madhya Pradesh, India-452017
Email: yadavgopal0902@gmail.com, raj rma@yahoo.co.in, glprajapati@ietdavv.edu.in
(Received: September 15, 2021; In format November 30, 2021; Revised: November 20, 2023; Accepted: November 25, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53226
Abstract
In this paper, the notion of complex-valued fuzzy b-metric space is introduced. In this newly developed structure, we have established a sucient condition for a sequence to be Cauchy. Moreover, under suitable conditions of contractive type, the existence and uniqueness of fixed points of self-maps are established in this structure. To demonstrate the validity of the hypothesis and the degree of generality of our results, some examples are also furnished.
2020 Mathematical Sciences Classification: 47H10, 54H25
Keywords and Phrases: Complex valued fuzzy metric, complex valued fuzzy b-metric space, t-norm, Cauchys sequence, fixed point.