Titlebook: Advances in Summability and Approximation Theory; S. A. Mohiuddine,Tuncer Acar Book 2018 Springer Nature Singapore Pte Ltd. 2018 Statistic

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,Approximation Properties of Chlodowsky Variant of (,,?,) Szász–Mirakyan–Stancu Operators,In the present paper, we introduce the Chlodowsky variant of (.,?.) Szász–Mirakyan–Stancu operators on the unbounded domain which is a generalization of (.,?.) Szász–Mirakyan operators. We have also derived its Korovkin-type approximation properties and rate of convergence.

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,Weighted Statistical Convergence of B?gel Continuous Functions by Positive Linear Operator,In the present work, we have introduced a weighted statistical approximation theorem for sequences of positive linear operators defined on the space of all real-valued .-continuous functions on a compact subset of .. Furthermore, we display an application which shows that our new result is stronger than its classical version.

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S. A. Mohiuddine,Tuncer AcarDiscusses the theory of classical and modern methods in summability.Includes a technique for studying the existence of solutions of infinite systems of differential equations in Banach sequence spaces

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Todd W. Neller,Taylor C. Nellerobtain some sufficient conditions, under which the existence of the limit . follows from that of .-., where . is a finite number. If . is a sequence of real numbers, then these Tauberian conditions are one-sided. If . is a sequence of complex numbers, these Tauberian conditions are two-sided. These

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L. Dusserre,J. P. Nakache,F. Grémye, we use the Hausdorff measure of noncompactness. Also, we give an example of infinite system of differential equations which has a solution in these spaces but has no solution in the classical Banach sequence spaces . and ..

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A Story About Computing with Roots of Unity361–369 (2013)). We establish a uniform convergence theorem and determine the degree of approximation in terms of the partial moduli of continuity of the approximated function. We estimate the error in simultaneous approximation of the function by the bivariate operators by using finite differences.

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Kathrin Schier,Simone Fischer-Hübnerthogonal expansions and discuss their approximation properties in the . space. We also investigate operators of Szász–Mirakjan type defined via Hermite polynomials. We give the rates of convergence by means of the modulus of continuity and moduli of smoothness. We present Voronovskaya type theorems