In this article, we introduce and study some difference sequence spaces of fuzzy numbers by making use of λ-statistical convergence of order (η, δ + γ) . With the aid of MATLAB software, it appears that the statistical convergence of order (η, δ + γ) is well defined every time when (δ + γ) > η and this convergence fails when (δ + γ) < η. Moreover, we try to set up relations between (Δv, λ)-statistical convergence of order (η, δ + γ) and strongly (Δv, p, λ)-Cesàro summability of order (η, δ + γ) and give some compelling instances to show that the converse of these relations is not valid. In addition to the above results, we also graphically exhibits that if a sequence of fuzzy numbers is bounded and statistically convergent of order (η, δ + γ) in (Δv, λ), then it need not be strongly (Δv, p, λ)-Cesàro summable of order (η, δ + γ).

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In this study, we deal with some new vector valued multiplier spaces $S_{G_{h}}(\sum_{k}z_{k})$ S G h ( ∑ k z k ) and $S_{wG_{h}}(\sum_{k}z_{k})$ S w G h ( ∑ k z k ) related with $\sum_{k}z_{k}$ ∑ k z k in a normed space Y. Further, we obtain the completeness of these spaces via weakly unconditionally Cauchy series in Y and $Y^{*}$ Y ∗ . Moreover, we show that if $\sum_{k}z_{k}$ ∑ k z k is unconditionally Cauchy in Y, then the multiplier spaces of $G_{h}$ G h -almost convergence and weakly $G_{h}-$ G h − almost convergence are identical. Finally, some applications of the Orlicz–Pettis theorem with the newly formed sequence spaces and unconditionally Cauchy series $\sum_{k}z_{k}$ ∑ k z k in Y are given.

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In this article, we introduce and study sequence spaces of Cesàro–Nörlund operators of order n associated with a sequence of Orlicz functions. We obtain some topological properties and Schauder basis of these sequence spaces. Moreover, we compute the α-, β- and γ-duals and the matrix transformations of these newly formed sequence spaces. Finally, we prove that these sequence spaces are of Banach–Saks type p and have a weak fixed-point property.

The purpose of this article is to study and investigate statistically probability convergence for the sequence of random variables by virtue of deferred Nörlund and deferred Euler summability mean. With the aid of MATLAB software, we also graphically exhibit the probability convergence for probability density function of random variables. Further, as an application of our newly formed summability mean, we prove Korovkin‐type approximation theorem via deferred Nörlund and deferred Euler statistically probability convergence and present compelling instances to illustrate the findings.

The purpose of this article is to study and investigate statistically probability convergence for the sequence of random variables by virtue of deferred N\“{o}rlund and deferred Euler summability mean. With the aid of MATLAB software, we also graphically exhibits the statistically probability convergence for probability density function of random variables. Further, as an application of our newly form summability mean, we prove Korovkin type approximation theorem via deferred N\”{o}rlund and deferred Euler statistically probability convergence and present compelling instances to illustrate the findings.

We introduce and study deferred Nörlund statistical convergence in probability, mean of order r, distribution and study the interrelation among them. Based upon the proposed method to illustrate the findings, we presented new Korovkin type theorems for the sequence of random variables via deferred Nörlund statistically convergence and present compelling examples to demonstrate the effectiveness of the results.2010 Mathematics Subject Classification. 40A05, 40A30.