Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 1537–1556 | Cite as

Approximation by a Class of q-Beta Operators of the Second Kind Via the Dunkl-Type Generalization on Weighted Spaces

  • H. M. SrivastavaEmail author
  • M. Mursaleen
  • Md. Nasiruzzaman


The aim of the present article is to study the approximation and other related properties of a class of q-Szász–Beta type operators of the second kind. In this context, we construct the class of q-Szász–Beta type operators of the second kind, which are generated by means of the exponential functions of the basic (or q-) calculus via the Dunkl-type generalization. In order to get a uniform convergence on weighted spaces, we obtain Korovkin-type approximation theorems involving local approximations and weighted approximations, the rate of convergence in terms of the classical, the second-order and the weighted moduli of continuity, as well as a set of direct theorems. Relevant connection of the results presented in this article with those in earlier works is also indicated.


Basic (or q-) calculus Basic (or q-) integers Basic (or q-) Beta functions Basic (or q-) exponential functions Dunkl’s analogue Generalized exponential functions Szász operator Modulus of continuity Peetre’s K-functional Weighted modulus of continuity Korovkin-type approximation theorems 

Mathematics Subject Classification

Primary 41A25 41A36 Secondary 33C45 



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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  2. 2.Department of Medical Research, China Medical University HospitalChina Medical UniversityTaichungPeople’s Republic of China
  3. 3.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  4. 4.Department of Computer Science (SEST)Jamia Hamdard UniversityHamdard NagarIndia

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