In this paper, we are dealing with a new type of Baskakov-Schurer-Szász operators (1.2). Approximation properties of this operators are explored: the rate of convergence in terms of the usual moduli of smoothness is given, the convergence in certain weighted spaces is investigated. We study q-analogues of Baskakov-Schurer-Szász operators and it's Stancu generalization. In the last section, we give better error estimations for the operators (6.3) using King type approach and obtained weighted statistical approximation properties for operator (9.1).
In this paper, we introduce a generalization of the Kantorovich-type Bernstein operators based on q-integers and get a Bohman-Korovkin-type approximation theorem of these operators. We also compute the rate of convergence using the first modulus of smoothness.
In the present paper, we consider Stancu type generalization of Baskakov-Kantorovich operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type function are also established for said operators. Finally, we construct a bivariate generalization of the operator and also obtain the statistical approximation properties.
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