Statistical approximation of Meyer--König and Zeller operators based on $q$-integers
Copyright policy )Statistical approximation of Meyer--König and Zeller operators based on $q$-integers
Summary: In this paper, we introduce a generalization of the Meyer-König and Zeller operators based on \(q\)-integers and get a Bohman-Korovkin type approximation theorem of these operators via \(A\)-statistical convergence. We also compute rate of \(A\)-statistical convergence of these \(q\)-type operators by means of the modulus of continuity and Lipschitz type maximal function, respectively. The second purpose of this note is to obtain explicit formulas for the monomials \(\big( \frac{t}{1-t}\big) ^{\nu }\), \(\nu =0,1,2\) of \(q\)-type generalization of Meyer-König and Zeller operators.
the Bollman-Korovkin type theorem, Approximation to limiting values (summation of series, etc.), \(q\)-integers, Approximation by positive operators, Rate of convergence, degree of approximation, the Bohman-Korovkin type theorem, q-integers, Approximation by polynomials, \(A\)-statistical convergence, modulus of continuity, A-statistical convergence, Lipschitz type maximal function, positive linear operators
the Bollman-Korovkin type theorem, Approximation to limiting values (summation of series, etc.), \(q\)-integers, Approximation by positive operators, Rate of convergence, degree of approximation, the Bohman-Korovkin type theorem, q-integers, Approximation by polynomials, \(A\)-statistical convergence, modulus of continuity, A-statistical convergence, Lipschitz type maximal function, positive linear operators
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