Korovkin-Type Approximation Theorem for Double Sequences of Positive Linear Operators via Statistical A-Summability

AbstractThe aim of this paper is to present a Korovkin-type approximation theorem on the space of all continuous real valued functions on any compact subset of the real two-dimensional space by using a A-summation process. We also study the rates of convergence of positive linear operators with the help of the modulus of continuity.

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A KOROVKIN TYPE APPROXIMATION THEOREM FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS OF TWO VARIABLES IN A-STATISTICAL SENSE

Bulletin of the Korean Mathematical Society ◽

10.4134/bkms.2010.47.4.825 ◽

2010 ◽

Vol 47 (4) ◽

pp. 825-837 ◽

Cited By ~ 5

Author(s):

Kamil Demirci ◽

Fadime Dirik

Keyword(s):

Approximation Theorem ◽

Linear Operators ◽

Positive Linear Operators ◽

Double Sequences ◽

Korovkin Type Approximation Theorem ◽

Type Approximation ◽

Statistical Sense

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

Filomat ◽

10.2298/fil1712749k ◽

2017 ◽

Vol 31 (12) ◽

pp. 3749-3760 ◽

Cited By ~ 5

Author(s):

Ali Karaisa ◽

Uğur Kadak

Keyword(s):

Statistical Convergence ◽

Approximation Theorem ◽

Linear Operators ◽

Positive Linear Operators ◽

Bernstein Operator ◽

Korovkin Type Approximation Theorem ◽

Type Approximation ◽

Inclusion Relations ◽

Prior Investigation

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.

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TRIANGULAR A−STATISTICAL RELATIVE UNIFORM CONVERGENCE FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi200309006c ◽

2021 ◽

pp. 065

Author(s):

Selin Çınar

Keyword(s):

Uniform Convergence ◽

Approximation Theorem ◽

Dimensional Space ◽

Linear Operators ◽

Two Dimensional ◽

Double Sequences ◽

The Real ◽

Korovkin Type Approximation Theorem ◽

Type Approximation ◽

Relative Uniform Convergence

In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences of functions defined on a compactsubset of the real two-dimensional space. Based upon this new convergencemethod, we prove Korovkin-type approximation theorem. Finally, we give some further developments.

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Korovkin-type approximation theorem for Bernstein Stancu operator of rough statistical convergence of triple sequence

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v38i7.45874 ◽

2019 ◽

Vol 38 (7) ◽

pp. 69-83

Author(s):

Ayten Esi ◽

Mustafa Kemal Ozdemir ◽

Nagarajan Subramanian

Keyword(s):

Statistical Convergence ◽

Approximation Theorem ◽

Linear Operators ◽

Positive Linear Operators ◽

Korovkin Type Approximation Theorem ◽

Type Approximation ◽

Increasing Function

We obtain a Korovkin-type approximation theorem for Bernstein Stancu polynomials of rough statistical convergence of triple sequences of positive linear operators of three variables from $H_{\omega}\left( K\right) $ to $C_{B}\left( K\right) $, where $K=[0,\infty)\times\lbrack0,\infty )\times\lbrack0,\infty)$ and $\omega$ is non-negative increasing function on $K$.

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Korovkin type approximation theorem for BBH type operators via J-convergence

Mathematica Slovaca ◽

10.2478/s12175-010-0053-3 ◽

2010 ◽

Vol 60 (6) ◽

Cited By ~ 2

Author(s):

Hüseyin Aktuğlu ◽

Mehmet Özarslan

Keyword(s):

Approximation Theorem ◽

Linear Operators ◽

Positive Linear Operators ◽

Korovkin Type Approximation Theorem ◽

Type Approximation

AbstractThis paper provides a Korovkin type approximation theorem for a class of positive linear operators including Bleimann-Butzer and Hahn operators via J-convergence.

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\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathfrak{B}$ \end{document} -statistical approximation for periodic functions

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2009.1133 ◽

2010 ◽

Vol 47 (3) ◽

pp. 321-332

Author(s):

Fadime Dirik ◽

Kamil Demirci

Keyword(s):

Statistical Convergence ◽

Approximation Theorem ◽

Continuous Functions ◽

Linear Operators ◽

Positive Linear Operators ◽

Statistical Approximation ◽

Periodic Functions ◽

Real Numbers ◽

Korovkin Type Approximation Theorem ◽

Type Approximation

In this study, using the concept of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathfrak{B}$$ \end{document}-statistical convergence for sequence of infinite matrices \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathfrak{B}$$ \end{document} = (\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathfrak{B}$$ \end{document}i ) with \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathfrak{B}$$ \end{document}i = ( bnk ( i )) we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on C * which is the space of all 2π-periodic and continuous functions on ℝ, the set of all real numbers. Also we study the rates of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathfrak{B}$$ \end{document}-statistical convergence of approximating positive linear operators.

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Statistical Approximation for Periodic Functions of Two Variables

Journal of Function Spaces and Applications ◽

10.1155/2013/491768 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5 ◽

Cited By ~ 4

Author(s):

Abdullah Alotaibi ◽

M. Mursaleen ◽

S. A. Mohiuddine

Keyword(s):

Statistical Convergence ◽

Approximation Theorem ◽

Linear Operators ◽

Positive Linear Operators ◽

Statistical Approximation ◽

Periodic Functions ◽

Korovkin Type Approximation Theorem ◽

Type Approximation ◽

Functions Of Two Variables ◽

Function Of Two Variables

We prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical summability(C,1,1). We also study the rate of statistical summability(C,1,1)of positive linear operators. Finally we construct an example to show that our result is stronger than those previously proved for Pringsheim's convergence and statistical convergence.

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