The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
In this paper, we are dealing with q-Bemstein-Durrmeyer-Stancu operators. Firstly, we have estimated moments of these operators. Then we have discussed some approximation properties and asymptotic formulas. We have ob...In this paper, we are dealing with q-Bemstein-Durrmeyer-Stancu operators. Firstly, we have estimated moments of these operators. Then we have discussed some approximation properties and asymptotic formulas. We have obtained better estimations by using King type approach and given statistical convergence for the operators.展开更多
In the present paper, we propose the q analogue of Szasz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergenc...In the present paper, we propose the q analogue of Szasz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the q operators. Voronovskaja type theorem is also obtained. Our results generalize and supplement some convergence results of the q-Szasz-Beta operators, thus they improve the existing results.展开更多
In this paper, we propose the q analogue of modified Baskakov-Beta operators. The Voronovskaja type theorem and some direct results for the above operators are discussed. The rate of convergence and weighted approxima...In this paper, we propose the q analogue of modified Baskakov-Beta operators. The Voronovskaja type theorem and some direct results for the above operators are discussed. The rate of convergence and weighted approximation by the operators are studied.展开更多
In this paper we introduce a new kind of Baskakov-Schurer-Szasz-Beta operators M^qn,p based on q-integers. We establish some direct results in the polynomial weighted space of continuous functions defined on the inter...In this paper we introduce a new kind of Baskakov-Schurer-Szasz-Beta operators M^qn,p based on q-integers. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞]. Then we obtain the estimates on the rate of convergence and weighted approximation of operators M^qn,p in terms of modulus of continuity.展开更多
In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obta...In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obtain point-wise estimate, using the Lipschitz type maximal function.展开更多
Using Hartogs'fundamental theorem for analytic functions in several complex variables,we establish a multiple q-exponential differential operational identity for the analytic functions in several variables,which c...Using Hartogs'fundamental theorem for analytic functions in several complex variables,we establish a multiple q-exponential differential operational identity for the analytic functions in several variables,which can be regarded as a multiple q-translation formula.This multiple q-translation formula is a fundamental result and play a pivotal role in q-mathematics.Using this q-translation formula,we can easily recover many classical conclusions in q-mathematics and derive some new q-formulas.Our work reveals some profound connections between the theory of complex functions in several variables and q-mathematics.展开更多
基金Supported by the National Natural Science Foundation of China（10771093） Supported by the Youth Foundation of Luoyang Normal College（2013-QNJJ-001） Supported by the Youth Foundation of the Luoyang Institute of Science and Technology（2012QZ05）
文摘The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
文摘In this paper, we are dealing with q-Bemstein-Durrmeyer-Stancu operators. Firstly, we have estimated moments of these operators. Then we have discussed some approximation properties and asymptotic formulas. We have obtained better estimations by using King type approach and given statistical convergence for the operators.
文摘In the present paper, we propose the q analogue of Szasz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the q operators. Voronovskaja type theorem is also obtained. Our results generalize and supplement some convergence results of the q-Szasz-Beta operators, thus they improve the existing results.
文摘In this paper, we propose the q analogue of modified Baskakov-Beta operators. The Voronovskaja type theorem and some direct results for the above operators are discussed. The rate of convergence and weighted approximation by the operators are studied.
文摘In this paper we introduce a new kind of Baskakov-Schurer-Szasz-Beta operators M^qn,p based on q-integers. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞]. Then we obtain the estimates on the rate of convergence and weighted approximation of operators M^qn,p in terms of modulus of continuity.
文摘In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obtain point-wise estimate, using the Lipschitz type maximal function.
基金Supported by the National Natural Science Foundation of China(Grant No.11971173)Science and Technology Commission of Shanghai Municipality(Grant No.22DZ2229014)。
文摘Using Hartogs'fundamental theorem for analytic functions in several complex variables,we establish a multiple q-exponential differential operational identity for the analytic functions in several variables,which can be regarded as a multiple q-translation formula.This multiple q-translation formula is a fundamental result and play a pivotal role in q-mathematics.Using this q-translation formula,we can easily recover many classical conclusions in q-mathematics and derive some new q-formulas.Our work reveals some profound connections between the theory of complex functions in several variables and q-mathematics.
