Extension of fixed point results in intuitionistic fuzzy b metric space

Article type: Research Article

Authors: Konwar, Nabanita^{; *}

Affiliations: Department of Mathematics, Assam University, Silchar, Cachar, Assam, India

Correspondence: [*] Corresponding author. Department of Mathematics, Assam University, Silchar, Cachar, Assam-788011, India E-mail: nabnitakonwar@gmail.com.

Abstract: The aim of this paper is to define the notion of intuitionistic fuzzy b metric space (in short, IFbMS) along with some useful results. We establish some important Lemmas in order to study the Cauchy sequence in IFbMS. To further develop the work, we establish some fixed point theorems and study the existence of unique fixed point of some self mappings in IFbMS. We also develop the concept of Ćirić quasi-Contraction theorem in IFbMS. Examples are provided to validate the non-triviality of the results.

Keywords: Intuitionistic fuzzy b-metric space, Cauchy sequence, fixed point theorem, unique fixed point, Ćirić quasi-contraction theorem

DOI: 10.3233/JIFS-201233

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 5, pp. 7831-7841, 2020