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1.
In this paper, we introduce the generalized q-Bernstein polynomials based on the q-integers and we study approximation properties of these operators. In special case, we obtain Stancu operators or Phillips polynomials.  相似文献   

2.
In the present paper we propose the q analogue of the modified Beta operators. We apply q-derivatives to obtain the central moments of the discrete q-Beta operators. A direct result in terms of modulus of continuity for the q operators is also established. We have also used the properties of q integral to establish the recurrence formula for the moments of q analogue of the modified Beta operators. We also establish an asymptotic formula. In the end we have also present the modification of such q operators so as to have better estimate.  相似文献   

3.
We are in progress of extending the family of ‘q-deformed operators’ considered in the previous papers by joining to them q-subnormal as well as q-formally subnormal ones. It turns out that q-positive definiteness, a notion generalizing Halmos' standard positive definiteness of bounded subnormal operators, is likewise central for our new scheme.  相似文献   

4.
We prove q-Taylor series for Jackson q-difference operators. Absolute and uniform convergence to the original function are proved for analytic functions. We derive interpolation results for entire functions of q-exponential growth which is less than lnq−1, 0<q<1, from its values at the nodes , a is a non-zero complex number with absolute and uniform convergence criteria.  相似文献   

5.
In this paper, we use the q-Chu–Vandermonde formula to prove two new operator identities, which are the extensions of Liu's results. These two q-exponential operator identities are used to derive some q-summation formulas and q-integrals.  相似文献   

6.
In the present paper, we introduce a Kantorovich type modification of q-Szász-Mirakjan operators and obtain weighted statistical approximation properties of these operators. Also for introduced operators, we give a Voronovskaja type theorem related to q-derivatives.  相似文献   

7.
In this paper, the approximation properties of q-Durrmeyer operators Dn,q(f;x) for fC[0,1] are discussed. The exact class of continuous functions satisfying approximation process limnDn,q(f;x)=f(x) is determined. The results of the paper provide an elaboration of the previously-known ones on operators Dn,q.  相似文献   

8.
In this paper q-Sobolev type spaces are defined on Rq by using the q-cosine Fourier transform and its inverse. In particular, embedding results for these spaces are established. Next we define the q-cosine potential and study some of its properties.  相似文献   

9.
In this paper, we apply q-exponential operator to get some general q-Chu-Vandermonde's identities.  相似文献   

10.
In this paper we show the equivalence between Goldman-Rota q-binomial identity and its inverse. We may specialize the value of the parameters in the generating functions of Rogers-Szegö polynomials to obtain some classical results such as Euler identities and the relation between classical and homogeneous Rogers-Szegö polynomials. We give a new formula for the homogeneous Rogers-Szegö polynomials hn(x,y|q). We introduce a q-difference operator θxy on functions in two variables which turn out to be suitable for dealing with the homogeneous form of the q-binomial identity. By using this operator, we got the identity obtained by Chen et al. [W.Y.C. Chen, A.M. Fu, B. Zhang, The homogeneous q-difference operator, Advances in Applied Mathematics 31 (2003) 659-668, Eq. (2.10)] which they used it to derive many important identities. We also obtain the q-Leibniz formula for this operator. Finally, we introduce a new polynomials sn(x,y;b|q) and derive their generating function by using the new homogeneous q-shift operator L(bθxy).  相似文献   

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