共查询到20条相似文献,搜索用时 28 毫秒
1.
Grzegorz Nowak 《Journal of Mathematical Analysis and Applications》2009,350(1):50-55
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.
Vijay Gupta 《Journal of Mathematical Analysis and Applications》2011,377(2):471-480
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.
Schôichi Ôta Franciszek Hugon Szafraniec 《Journal of Mathematical Analysis and Applications》2007,329(2):987-997
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 f∈C[0,1] are discussed. The exact class of continuous functions satisfying approximation process limn→∞Dn,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.
Jian-Ping Fang 《Journal of Mathematical Analysis and Applications》2008,339(2):845-852
In this paper, we apply q-exponential operator to get some general q-Chu-Vandermonde's identities. 相似文献
10.
Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah–Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah–Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities. 相似文献
11.
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
12.
In this paper, we first give two interesting operator identities, and then, using them and the q-exponential operator technique to some terminating summation formulas of basic hypergeometric series and q-integrals, we obtain some q-series identities and q-integrals involving 3?2. 相似文献
13.
Ahmed Fitouhi 《Journal of Mathematical Analysis and Applications》2007,328(1):518-534
In this paper, we study in quantum calculus the correspondence between poles of the q-Mellin transform (see [A. Fitouhi, N. Bettaibi, K. Brahim, The Mellin transform in Quantum Calculus, Constr. Approx. 23 (3) (2006) 305-323]) and the asymptotic behaviour of the original function at 0 and ∞. As applications, we give a new technique (in q-analysis) to derive the asymptotic expansion of some functions defined by q-integrals or by q-harmonic sums. Finally, a q-analogue of the Mellin-Perron formula is given. 相似文献
14.
The paper deals with a sequence of linear positive operators introduced via q-Calculus. We give a generalization in Kantorovich sense of its involving qR-integrals. Both for discrete operators and for integral operators we study the error of approximation for bounded functions and for functions having a polynomial growth. The main tools consist of the K-functional in Peetre sense and different moduli of smoothness. 相似文献
15.
Néji Bettaibi Fethi Bouzeffour 《Journal of Mathematical Analysis and Applications》2008,342(2):1203-1219
This paper is devoted to the study of some q-harmonic analysis related to the third q-Bessel function of order zero. We establish a product formula leading to a q-translation with some positive kernel. As an application, we provide a q-analogue of the continuous wavelet transform related to this harmonic analysis. 相似文献
16.
Yilmaz Simsek 《Journal of Mathematical Analysis and Applications》2006,318(1):333-351
The main purpose of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Riemann zeta function, q-analogue Hurwitz zeta function, q-analogue Dirichlet L-function and two-variable q-L-function. In particular, by using these generating functions, we will construct new generating functions which produce q-Dedekind type sums and q-Dedekind type sums attached to Dirichlet character. We also give the relations between these sums and Dedekind sums. Furthermore, by using *-product which is given in this paper, we will give the relation between Dedekind sums and q-L function as well. 相似文献
17.
Fethi Bouzeffour 《Journal of Mathematical Analysis and Applications》2007,336(2):833-848
We study fractional transforms associated with q-Bessel operator which is useful to inverse q-Riemann-Liouville and q-Weyl transforms. 相似文献
18.
A special case of the big q-Jacobi polynomials Pn(x;a,b,c;q), which corresponds to a=b=−c, is shown to satisfy a discrete orthogonality relation for imaginary values of the parameter a (outside of its commonly known domain 0<a<q−1). Since Pn(x;qα,qα,−qα;q) tend to Gegenbauer (or ultraspherical) polynomials in the limit as q→1, this family represents another q-extension of these classical polynomials, different from the continuous q-ultraspherical polynomials of Rogers. For a dual family with respect to the polynomials Pn(x;a,a,−a;q) (i.e., for dual discrete q-ultraspherical polynomials) we also find new orthogonality relations with extremal measures. 相似文献
19.
J. Arvesú 《Journal of Computational and Applied Mathematics》2010,233(6):1462-1469
This contribution deals with multiple orthogonal polynomials of type II with respect to q-discrete measures (q-Hahn measures). In addition, we show that this family of multiple orthogonal polynomials has a lowering operator, and raising operators, as well as a Rodrigues type formula. The combination of lowering and raising operators leads to a third order q-difference equation when two orthogonality conditions are considered. An explicit expression of this q-difference equation will be given. Indeed, this q-difference equation relates polynomials with a given degree evaluated at four consecutive non-uniformed distributed points, which makes these polynomials interesting from the point of view of bispectral problems. 相似文献
20.
Hjalmar Rosengren 《Journal of Combinatorial Theory, Series A》2008,115(3):376-406
We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic hypergeometric series, and as determinants and pfaffians of continuous q-ultraspherical or continuous q-Jacobi polynomials. As special cases, we obtain simple closed formulas for staircase-type partitions. 相似文献