The notion of statistical convergence has fascinated many researchers due mainly to the fact that it is more general than the well-established hypothesis of ordinary (classical) convergence. This work aims to investigate and present (presumably new) the statistical versions of Deferred weighted Riemann integrability and Deferred weighted Riemann summability for sequences of fuzzy functions. We first interrelate these two lovely theoretical notions by establishing an inclusion theorem. We then state and prove two fuzzy Korovkin-type theorems based on our proposed helpful and potential notions. We also demonstrate that our results are the nontrivial extensions of several known fuzzy Korovkin-type approximation theorems given in earlier works. Moreover, we estimate the statistically Deferred weighted Riemann summability rate supported by another promising new result. Finally, we consider several interesting exceptional cases and illustrative examples supporting our definitions and the results presented in this paper.

In this paper, we define strong Deferred summability and Deferred statistical summability in intuitionistic fuzzy \(n\)-normed linear spaces (briefly called IF-\(n\)-NLS) and study some of their properties. We also define Deferred statistical Cauchy sequence Deferred statistical completeness and characterize Deferred statistical summability in such spaces. Finally, we will compare Deferred statistical summability for different pairs of sequences $\alpha(\ell)$, $\gamma(\ell)$,$u(\ell)$ and $v(\ell)$ satisfying $\alpha(\ell) \leq u(\ell) < v(\ell) \leq \gamma(\ell)$.

Korovkin type approximation theorems are useful tools to check whether a given sequence (Ln) n³1 of positive linear operators on C[0,1] of all continuous functions on the real interval [0,1] is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions 1, x and x2 in the space C[0,1] as well as for the functions 1, cos and sin in the space of all continuous 2p-periodic functions on the real line. In this paper, we use the notion of statistical lacunary summability to improve the result of [Ann. Univ. Ferrara, 57 (2) (2011) 373-381] by using the test functions 1, e-x, e-2x n place of 1, x and x2. We apply the classical Baskakov operator to construct an example in support of our main result.

In this paper, we introduce the notion of Deferred statistical convergence in the neutrosophic normed spaces as an extension of statistical convergence, $\lambda$-statistical convergence, and lacunary statistical convergence. We investigate a few fundamental properties of the newly introduced notion. Finally, we introduce the concept of Deferred statistical Cauchy sequence and show that Deferred statistical Cauchy sequences are equivalent to Deferred statistical convergent sequences in the neutrosophic normed spaces.

This paper introduces the idea of Deferred-statistical A-convergence of order β of the sequence of  fuzzy numbers by using  a regular matrix Aand Deferred Ces\`{a}ro mean $D_{p,q}$. Also,  we establish some relations between the proposed idea and the strong  Deferred A-summability of  sequences of fuzzy  numbers. As an application, we apply this newly  statistical convergence for proving fuzzy Korovkin-type approximation theorem. Some illustrative examples are provided to justify the results obtained from this investigation.

In this study we introduce the concepts of statistical convergence of order b and strong p-Cesaro summability of order b for sequences of fuzzy numbers. Also, we give some relations between the statistical convergence of order b and strong p-Cesaro summability of order b and construct some interesting examples.

We obtain sufficient conditions for the series Sanln to be absolutely summable of order k by a triangular matrix.

The object of this paper is to establish a summability factor theorem for summability |A,d|k, k³1 where A is the lower triangular matrix with non-negative entries satisfying certain conditions.