Fuzzy Positive Linear Operators Research Articles

Some fuzzy Korovkin type approximation theorems via power series summability method

This article provides a power series summability-based Korovkin type approximation theorem for any sequence of fuzzy positive linear operators. Using the notion of fuzzy modulus of smoothness, we also derive an associated approximation theorem concerning the fuzzy rate of convergence of these operators. Furthermore, through an example, we illustrate that our summability- based Korovin type theorem has an advantage over the fuzzy Korovkin type theorem proved in the seminal paper by Anastassiou (Stud. Univ. Babeş-Bolyai Math L(4):3–10, 2005)

Weighted (λ,μ)-statistical convergence and statistical summability methods of double sequences of fuzzy numbers with application to Korovkin-type fuzzy approximation theorem

The paper aims to investigate different types of weighted statistical convergence and weighted statistical summability of double sequences of fuzzy numbers. Relations connecting statistical convergence and statistical summability have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. Relevant inclusion relations and related results concerning the new fuzzy summability methods have also been examined in detail. Finally, a Korovkin-type approximation theorem for double sequences of fuzzy positive linear operators has been established using the most generalized version of the summability method and showed its efficiency by means of a concrete example.

Statistical weighted mean summability of double sequences of fuzzy numbers

In this paper, we present statistical weighted mean ( briefly, (N?,p,q,1,1)) summability method for double sequences of fuzzy numbers and give necessary and sufficient Tauberian conditions under which statistical convergence of a double sequence of fuzzy numbers follows from its statistical (N?,p,q,1,1) summability. Furthermore, we apply our new method of summability to prove a fuzzy Korovkin type approximation theorem for a double sequence of fuzzy positive linear operators.

Weighted λ-statistical convergence connecting a statistical summability of sequences of fuzzy numbers and Korovkin-type approximation theorems

In this paper, we investigated the notion of generalized weighted λ-statistical convergence connecting $$ \left( {\bar{N}_{\lambda } , p_{n} } \right)^{F} $$ -statistical summability of sequences of fuzzy numbers. Some inclusion relations and other related results for the new summability methods are also given. Furthermore, we give a Korovkin-type approximation theorem for fuzzy positive linear operators using the notion of generalized weighted $$ \left( {\bar{N}_{\lambda } , p_{n} } \right)^{F} $$ -statistical summability.

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

On statistical summability (N¯,P) of sequences of fuzzy numbers

In this paper we introduce the concept of statistical summability (N?,p) of sequences of fuzzy numbers. We also present Tauberian conditions under which statistical convergence of a sequence of fuzzy numbers follows from its statistical summability (N?,p). Furthermore, we prove a Korovkin-type approximation theorem for fuzzy positive linear operators by using the notion of statistical summability (N?,p).

Four-dimensional matrix transformation and A-statistical fuzzy Korovkin type approximation

Abstract In this paper, we prove a fuzzy Korovkin-type approximation theorem for fuzzy positive linear operators by using A-statistical convergence for four-dimensional summability matrices. Also, we obtain rates of A-statistical convergence of a double sequence of fuzzy positive linear operators for four-dimensional summability matrices.

Statistical fuzzy approximation by fuzzy positive linear operators

In this paper, we prove a Korovkin-type approximation theorem for fuzzy positive linear operators by using the notion of A -statistical convergence, where A is a non-negative regular summability matrix. This type of approximation enables us to obtain more powerful results than in the classical aspects of approximation theory settings. An application of this result is also given. Furthermore, we compute the rates of this statistical fuzzy convergence of the operators via the fuzzy modulus of continuity.