Approximation of new bounded operators in intuitionistic fuzzy n-Banach spaces

Article type: Research Article

Authors: Konwar, Nabanita^a | Davvaz, Bijan^b | Debnath, Pradip^{c; *}

Affiliations: [a] Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh, India | [b] Department of Mathematics, Yazd University, Yazd, Iran | [c] Department of Applied Science and Humanities, Assam University, Silchar, Cachar, India

Correspondence: [*] Corresponding author. Pradip Debnath, Department of Applied Science and Humanities, Assam University, Silchar, Cachar - 788011, India. Tel.: +91 8575 158469; Fax: +91 3602 258533. E-mails: pradip.debnath@aus.ac.in and pdn@nerist.ac.in.

Abstract: In this paper we study approximation properties (APs) and bounded approximation properties (BAPs) in the setting of intuitionistic fuzzy n-Banach spaces (IFnBSs). Further, we define strong intuitionistic fuzzy n-continuous and strong intuitionistic fuzzy n-bounded operators and using them we prove the existence of an IFnBS with AP. In addition, we provide examples which show that there exist IFnBSs with the AP which fail to have the BAP.

Keywords: Intuitionistic fuzzy n-Banach space; approximation property, bounded approximation property.

DOI: 10.3233/JIFS-181094

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 6, pp. 6301-6312, 2018