Applications of deferred Cesàro statistical convergence of sequences of fuzzy numbers of order (ξ, ω)

Abstract

The purpose of this article is to study deferred Cesrào statistical convergence of order (ξ, ω) associated with a modulus function involving the concept of difference sequences of fuzzy numbers. The study reveals that the statistical convergence of these newly formed sequence spaces behave well for ξ ≤ ω and convergence is not possible for ξ > ω. We also define p-deferred Cesàro summability and establish several interesting results. In addition, we provide some examples which explain the validity of the theoretical results and the effectiveness of constructed sequence spaces. Finally, with the help of MATLAB software, we examine that if the sequence of fuzzy numbers is bounded and deferred Cesàro statistical convergent of order (ξ, ω) in (Δ, F, f), then it need not be strongly p-deferred Cesàro summable of order (ξ, ω) in general for 0 < ξ ≤ ω ≤ 1.

A Certain Class of Equi-Statistical Convergence in the Sense of the Deferred Power-Series Method

“…In view of the requirements (i) and (ii) of Theorem 5 along with Lemma 2, the final inequality (19) leads us to the assertion (18) of our Theorem 5. Hence, Theorem 5 is proved.…”

“…Again, in that year, Saini et al [17] also studied the results on equi-statistical convergence via the deferred Cesàro and deferred Euler summability product means with associated Korovkin-type theorems. Additionally, Saini et al [18] again studied deferred Riesz statistical convergence of a complex uncertain sequence with its applications; also in that year, Sharma et al [19] demonstrated the implementations of statistical deferred Cesàro convergence of fuzzy number valued sequences of order (ξ, ω). In the year 2018, Srivastava et al [20] studied and investigated the idea of sequences that converge equi-statistically based on the deferred Nörlund mean.…”