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The second and third powers of the Dirichlet kernel are used to construct discrete linear operators for the approximation of continuous periodic functions. An estimate of the rate of convergence is given. Approximation of non-periodic functions are also considered. [ABSTRACT FROM AUTHOR]

We study the pointwise degree of approximation of periodic functions of bounded variation by positive linear polynomial operators. For the proof we used sub-additive majorants. [ABSTRACT FROM AUTHOR]

With the help of generating functions, we present general conditions to construct positive linear operators which reproduce linear functions. The results are used to present a modification of the Cheney and Sharma operators and the rate of convergence is studied. [ABSTRACT FROM AUTHOR]

Abstract: We present direct theorems for some sequences of positive linear operators in weighted spaces. The results, given in terms of some Ditzian–Totik moduli of smoothness, include estimations in norms and Becker type estimations. [Copyright &y& Elsevier]

Abstract: For a function , we prove that where denotes a Ditzian–Totik-type modulus of order 2. We apply this result to obtain an asymptotic property for positive linear operators related to Voronovskaja type formulae. [Copyright &y& Elsevier]

Abstract: We estimate the constants related with the direct result for positive linear operators which preserves linear functions. The estimates are presented for the modulus of smoothness , where the weight φ is a function such that is concave. [Copyright &y& Elsevier]