Continuity and Banach contraction principle in intuitionistic fuzzy n-normed linear spaces

Article type: Research Article

Authors: Konwar, Nabanita | Debnath, Pradip^{; *}

Affiliations: Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh, India

Correspondence: [*] Corresponding author. Pradip Debnath, Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli 791109, Arunachal Pradesh, India. Tel.: +91 8575 158469; Fax: +91 3602 258533; E-mail: pdn@nerist.ac.in.

Abstract: In classical functional analysis, continuous mappings are essential for the study of many important theorems such as open mapping theorem, closed graph theorem and uniform boundedness theorem. These results are yet to be established in the general setting of an intuitionistic fuzzy n-normed linear space (IFnNLS). This motivates us to introduce the notion of continuous linear operators in this generalized setting. Furthermore, we establish the uniform continuity theorem and Banach’s contraction principle in an IFnNLS.

Keywords: Intuitionistic fuzzy n-normed linear space, intuitionistic fuzzy continuous linear operator, Banach contraction principle

DOI: 10.3233/JIFS-17500

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 4, pp. 2363-2373, 2017