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Fuzzy Bernstein Stancu difference operator of rough $I$-core of double sequences with weighted statistical convergence and its applications

Bipan Hazarika|N. Subramanian|A. Indumathi|A. Esi
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2020.08|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제20권 제1호|pp. 29-53|DOI 10.30948/afmi.2020.20.1.29

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키워드

difference operatorWeighted statistical convergencerough $I$-convergencefuzzy Bernstein Stancu polynomialsfuzzy Korovkin-type approximation theorem

초록

We introduce the notions of weighted statistical convergence and strong weighted summability of order $\beta $ for fuzzy Bernstein Stancu polynomials of difference operator of rough $I$-convergent of double sequence, and establish the relationship between them and also study the set of all fuzzy Bernstein Stancu polynomials of difference operator of rough $I$-limits of a double sequence spaces and relation between analyticness and fuzzy Bernstein Stancu polynomials of difference operator of rough $I$-core of a double sequence spaces. Finally, as an application, we appy our notion of weighted $\Delta ^{r}\left( p,q\right)$-statistical of order $\beta $ with a view of fuzzy Korovkin-type approximation theorem, discuss example to illustrate our approximation results.

Abstract

We introduce the notions of weighted statistical convergence and strong weighted summability of order $\beta $ for fuzzy Bernstein Stancu polynomials of difference operator of rough $I$-convergent of double sequence, and establish the relationship between them and also study the set of all fuzzy Bernstein Stancu polynomials of difference operator of rough $I$-limits of a double sequence spaces and relation between analyticness and fuzzy Bernstein Stancu polynomials of difference operator of rough $I$-core of a double sequence spaces. Finally, as an application, we appy our notion of weighted $\Delta ^{r}\left( p,q\right)$-statistical of order $\beta $ with a view of fuzzy Korovkin-type approximation theorem, discuss example to illustrate our approximation results.

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