Invariant convergent and invariant ideal convergent sequence in intuitionistic fuzzy normed space

Article type: Research Article

Authors: Khan, Vakeel A.^a | Ali Khan, Izhar^a | Esi, Ayhan^{b; *} | Alam, Masood^c

Affiliations: [a] Department of Mathematics, Aligarh Muslim University, Aligarh, India | [b] Malatya Turgut Ozal University, Engineering Facult, Department of Basic Engineering Science (Math.Sect.), Malatya, Turkey | [c] Department of Mathematics and IT Center for Preparatory Studies, Sultan Qaboos University, Sultanate of Oman

Correspondence: [*] Corresponding author. Ayhan Esi, Malatya Turgut Ozal University, Engineering Facult, Dept.of Basic Eng.Sci (Math.Sect.) 44040, Malatya, Turkey. E-mails: aesi23@hotmail.com; ayhan.esi@ozal.edu.tr.

Abstract:  The main purpose of this paper is to introduce invariant convergence in intuitionistic fuzzy normed space. Following which we present some characteristics of this notion with respect to intuitionistic fuzzy norm. We also define strongly invariant convergence, ideal invariant convergence and invariant ideal convergence in intuitionistic fuzzy normed space. After that, we establish the relationship between these notions with respect to intuitionistic fuzzy norm. Lastly, we define ideal invariant Cauchy and invariant ideal Cauchy criteria for sequences in intuitionistic fuzzy normed space and relate it to their convergence notion.

Keywords: Intuitionistic fuzzy normed space, Ideal convergent, Invariant mean

DOI: 10.3233/JIFS-213327

Journal: Journal of Intelligent & Fuzzy Systems, vol. 43, no. 1, pp. 1429-1438, 2022