## 2 Preliminaries  
Let \((C,1)\) be the mean [2] of the sequence \(v=(v_{\rho})\); thus, we have  
\[\sigma_{\rho}=\frac{1}{\rho+1}\sum_{i=0}^{v}v_{i}.\]  
Subsequently, the deferred Cesaro method for sequences is given as follows:  
Let \((a_{\rho})\) and \((b_{\rho})\in\mathbb{Z}^{0+}\) be such that  
\[a_{\rho}<b_{\rho},\;\rho\in\mathbb{N}\quad\text{and}\quad\lim_{\rho\to\infty}b _{\rho}=\infty.\]  
The deferred Cesaro \(D(a_{\rho},b_{\rho})\)-mean (see [PERSON] [5]) of a sequence \((v_{\rho})\) is given by  
\[D(a_{\rho},b_{\rho}) =\frac{v_{a_{\rho}+1}+v_{a_{\rho}+2}+v_{a_{\rho}+3}+\cdots+v_{b_{ \rho}}}{b_{\rho}-a_{\rho}}\] \[=\frac{1}{b_{\rho}-a_{\rho}}\sum_{i=a_{\rho}+1}^{b_{\rho}}v_{i}.\]  
In recent years, statistical convergence has gained considerable importance, often being preferred over usual convergence due to its broader applicability. This development can be traced back to the foundational contributions of [PERSON] [6] and [PERSON] [7], who expanded the theoretical framework of statistical convergence. Nowadays, this concept plays a vital part in various areas of mathematics, as well as analytical statistics. It has significant applications in disciplines such as data science, industrial mathematics, computational algebra, and cryptography. For further details, readers may refer to [8; 9]. Suppose \(\mathcal{H}\subseteq\mathbb{N}\), setting  
\[\mathcal{H}_{\rho}:=\{\rho:\rho\leqq\tau\quad\text{and}\quad\rho\in\mathbb{N}\}. \tag{1}\]Thus, the asymptotic density \(d(\mathcal{H})\) of \(\mathcal{H}\) is specified by  
\[d(\mathcal{H})=\lim_{\rho\to\infty}\frac{|\mathcal{H}_{\rho}|}{\rho}=a, \tag{2}\]  
where \(|\mathcal{H}_{\rho}|\) represents the number of elements in the set \(\mathcal{H}_{\rho}\). Definition 1: A given sequence \((v_{\rho})\) converges statistically to a finite number \(\kappa\) if, for all \(\epsilon>0\),  
\[\mathcal{H}_{\epsilon}=\left\{\rho\in\mathbb{N}\quad\text{and}\quad\left|v_{ \rho}-\kappa\right|\geqq\epsilon\right\}\]  
ensures zero asymptotic density (see [6; 7]). That is, for every \(\epsilon>0\),  
\[d\big{(}\mathcal{H}_{\epsilon}\big{)}=\frac{|\mathcal{H}_{\epsilon}|}{\rho}=0 \quad\text{as }\rho\to\infty.\]  
If the limit exist, we denote this as  
\[\text{stat}\lim v_{\rho}=\kappa.\]  
Definition 2: Let \((a_{\rho})\) and \((b_{\rho})\in\mathbb{Z}^{0+}\). A sequence \((v_{\rho})\) is deferred to as statistically convergent \((\text{stat}_{\text{D}})\) to \(\kappa\) if, for all \(\epsilon>0\),  
\[\mathcal{H}_{\epsilon}=\left\{a_{\rho}\leqq b_{\rho}\quad\text{and}\quad \left|v_{\rho}-\kappa\right|\geqq\epsilon\right\}\]  
ensures zero asymptotic density. That is, for all \(\epsilon>0\),  
\[a_{\rho}<b_{\rho},\;\rho\in\mathbb{N}\quad\text{and}\quad\lim_{\rho\to\infty}b _{\rho}=\infty.\]0  
We write  
\[a_{\rho}<b_{\rho},\;\rho\in\mathbb{N}\quad\text{and}\quad\lim_{\rho\to\infty}b _{\rho}=\infty.\]1  
In the latter half of the twentieth century, numerous researchers made significant contributions to the development of statistical convergence. [PERSON] [10] investigated statistically convergent sequences of real numbers, particularly their boundedness properties. [PERSON] [6] formalized the Cauchy criterion for statistical convergence and established fundamental results using summability techniques. [PERSON] [11] expanded this research by exploring statistical convergence in locally convex spaces, leading to several important insights. Building upon these advancements, [PERSON] and [PERSON] [12] introduced the notion of lacunary statistical summability for sequences of real numbers, which paved the way for further significant developments in the field. The concept of Cesaro summability in the statistical sense, along with its applications, was originally introduced by [PERSON] [13]. [PERSON] et al. [14] expanded on this foundation by presenting significant results on statistical summability means, supported by illustrative examples, and by proving related Korovkin-type theorems.