In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic nornied space, and the notion of probabilistic distance between the operators, which describes the above conv...In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic nornied space, and the notion of probabilistic distance between the operators, which describes the above convergence completely. In terms of these notions, we obtained the essential features of the continuity of operators, and of the uniform convergence of operator sequences, and we also obtained the closure of continuity and complete continuity under the operation of the limit of uniform convergence.展开更多
In the present paper, we consider Stancu type generalization of the summation integral type operators discussed in [15]. We apply hypergeometric series for obtaining moments of these operators. We also discuss about a...In the present paper, we consider Stancu type generalization of the summation integral type operators discussed in [15]. We apply hypergeometric series for obtaining moments of these operators. We also discuss about asymptotic formula and error estimation in terms of modules of continuity.展开更多
In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of ...In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of continuity of these positive linear operators. Finally, we obtain the rate of statistical convergence of truncated operators.展开更多
In this paper we shall defin a kind of generalized Szász-Mirakjan operator and discuss its convergence and degree of approximation,extend some results got by J.Grof^[1] and Z.Ditzian^[2].
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
文摘In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic nornied space, and the notion of probabilistic distance between the operators, which describes the above convergence completely. In terms of these notions, we obtained the essential features of the continuity of operators, and of the uniform convergence of operator sequences, and we also obtained the closure of continuity and complete continuity under the operation of the limit of uniform convergence.
文摘In the present paper, we consider Stancu type generalization of the summation integral type operators discussed in [15]. We apply hypergeometric series for obtaining moments of these operators. We also discuss about asymptotic formula and error estimation in terms of modules of continuity.
文摘In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of continuity of these positive linear operators. Finally, we obtain the rate of statistical convergence of truncated operators.
文摘In this paper we shall defin a kind of generalized Szász-Mirakjan operator and discuss its convergence and degree of approximation,extend some results got by J.Grof^[1] and Z.Ditzian^[2].
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
