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Korovkin Type Approximation Theorem for Almost and Statistical Convergence
Springer Optimization and Its Applications, 2012In this paper, we use the notion of almost convergence and statistical convergence to prove the Korovkin type approximation theorem by using the test functions 1,e −x ,e −2x . We also display an interesting example in support of our results.
M Mursaleen, S A Mohiuddine
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Statistical Relatively Equal Convergence and Korovkin-Type Approximation Theorem
Results in Mathematics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fadime Dirik
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On ideal summability and a Korovkin type approximation theorem
The Journal of Analysis, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bipan Hazarika, Ayhan Esi
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A new generalized version of Korovkin-type approximation theorem
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022In statistical convergence, the convergence condition is obtained just for a majority of elements. Therefore it extends the concept of ordinary convergence and it is an effective tool to obtain strong results. Recently, there have been obtained many generalizations of statistical convergence by combining it with ideal, measure and mean.
Vakeel A. Khan +2 more
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Weighted statistical convergence and its application to Korovkin type approximation theorem
Applied Mathematics and Computation, 2012A sequence \(x=(x_k)\) is said to be statistically convergent to \(L\), \(L=st-\lim x\), if and only if for all \(\varepsilon>0\) the set \(K_\varepsilon=\{k\in\mathbb N: |x_k-L|\geq\varepsilon\}\) has natural density zero. If \(p=(p_k)\) is a sequence of nonnegative integers, with \(p_0>0\) and \(P_n=\sum^n_0 p_k\to +\infty\) as \(n\to+\infty\), and ...
M Mursaleen +2 more
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Quantitative Korovkin type theorems on simultaneous approximation
Mathematische Zeitschrift, 1984 Let K = [-a, b] be a compact interval of the real axis, and K ' = [-c, d] be a subinterval of K. By X = C(K), r>O, we denote the Banach space of realvalued and r-times continuously differentiable functions on K, equipped with norm given by IlgHx:= max {[IDJgl[K}. Here D ~ is the j-th differential operator, o=
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Korovkin type approximation theorems obtained through generalized statistical convergence
Applied Mathematics Letters, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S A Mohiuddine, Abdullah K Noman
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Korovkin type approximation theorems on the space of continuously differentiable fnctions
Approximation Theory and its Applications, 2000The authors impose four equivalent norms on the space of continuously differentiable functions on \([0,1]\). The norms are \(\|f\|_M:=\max \{\|f\|_\infty,\|f'\|_\infty\}\), \(\|f\|_0:=|f(0)|+\|f'\|_\infty\), \(\|f\|_c:=\||f(\cdot)|+|f'(\cdot)|\|_\infty\), and \(\|f\|_\Sigma:= \|f\|_\infty+\|f'\|_\infty\). They show that the set \(\{1,x,x^2,x^3\}\) is a
Hirasawa, Go +2 more
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A Korovkin type approximation theorems via $$\mathcal{I}$$ -convergence
Czechoslovak Mathematical Journal, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Statistical lacunary summability and a Korovkin type approximation theorem
ANNALI DELL'UNIVERSITA' DI FERRARA, 2011The natural density of a subset \(K\) of the natural numbers is given by \(\lim_n |K_n|/n\), where \(K_n=\{k\leq n: k\in K\}\), if this limit exists. A sequence of real numbers \(\{x_k\}^\infty_1\) is statistically convergent to \(L\) iff for all \(\varepsilon>0\), \(K_\varepsilon=: \{k\in\mathbb N: |x_k-L|\geq\varepsilon\}\) has natural density zero ...
Mursaleen, M., Alotaibi, A.
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