Ideal convergent sequence spaces of fuzzy star–shaped numbers

Article type: Research Article

Authors: Khan, Vakeel A.^{a; *} | Tuba, Umme^a | Ashadul Rahaman, SK.^a | Ahmad, Ayaz^b

Affiliations: [a] Department of Mathematics, Aligarh Muslim University, Aligarh, India | [b] Department of Mathematics, National Institute of Technology, Patna, India

Correspondence: [*] Corresponding author. Vakeel A. Khan, Department of Mathematics, Aligarh Muslim University, Aligarh–202002, India. E-mail: vakhanmaths@gmail.com.

Abstract: In 1990, Diamond [16] primarily established the base of fuzzy star–shaped sets, an extension of fuzzy sets and numerous of its properties. In this paper, we aim to generalize the convergence induced by an ideal defined on natural numbers ℕ , introduce new sequence spaces of fuzzy star–shaped numbers in ℝn and examine various algebraic and topological properties of the new corresponding spaces as well. In support of our results, we provide several examples of these new resulting sequences.

Keywords: Fuzzy star–shaped numbers, L_p–metric, I–convergence, solidity and convergence free

DOI: 10.3233/JIFS-202534

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 6, pp. 11355-11362, 2021