Approximation by a Class of q-Beta Operators of the Second Kind Via the Dunkl-Type Generalization on Weighted Spaces
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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.
KeywordsBasic (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 ClassificationPrimary 41A25 41A36 Secondary 33C45
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