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Commentationes Mathematicae
EN The aim of this paper is to study a bivariate version of the operator investigated in [2], [4]. We shall present Voronovskaya type theorem and theorems giving a rate of convergence of this operator. Some applications for the limit problem are indicated.
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Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
1999 [Z] 39 225-245
EN In this paper we study a certain elliptic operator defined by appropriate sums and prove the formula for ellipsoidal mean value. Using this expansion we obtain direct and reverse theorems on the mean value for solutions of the iterated linear equation (L-aźa)(m)u=0. Similar problems are studied for [...]
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Demonstratio Mathematica
FR Dans cette note on demontre une variante du theoreme de Cauchy de la valeur moyenne.
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Demonstratio Mathematica
2005 Vol. 38, nr 1 143--151
EN In this paper we consider the continuous version of the operator investigated by Mazhar and Totik ([2]). Some applications for the limit problem are indicated.
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Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
2000 [Z] 40 181-189
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Commentationes Mathematicae
EN In this paper we will study some approximate properties of Baskakov-Durrmeyer type operators Mα,an. We determine the rate of convergence and prove the Voronovskaya type theorem for those operators.
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Opuscula Mathematica
EN The Cartan-Monge geometric approach to the characteristics method for Hamilton-Jacobi type equations and nonlinear partial differential equations of higher orders is analyzed. The Hamiltonian structure of characteristic vector fields related with nonlinear partial differential equations of first ord[...]
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Demonstratio Mathematica
2014 Vol. 47, nr 2 336--349
EN In the present paper, we investigate the convergence and the approximation order of some Durrmeyer type operators in exponential weighted space. Furthermore, we obtain the Voronovskaya type theorem for these operators.
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Opuscula Mathematica
EN The generalized Cartan-Monge type approach to the characteristics method is discussed from the geometric point of view. Its application to the classical one-dimensional linear heat equation Ut - uxx = 0 is presented. It is shown that the corresponding exact solution of the Cauchy problem can be repr[...]
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