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Approximation of Some Classes of Functions by Landau Type Operators
(Birkhauser, 2021) Agratini, Octavian; Aral, Ali
This paper aims to highlight a class of integral linear and positive operators of Landau type which have affine functions as fixed points. We focus to reveal approximation properties both in Lp spaces and in weighted Lp spaces (1 ? p< ?). Also, we give an extension of the operators to approximate real-valued vector functions. In this case, the study pursues the approximation of continuous functions on convex compacts. The evaluation of the rate of convergence in one and multidimensional cases is performed by using adequate moduli of smoothness. © 2020, Springer Nature Switzerland AG.
On two classes of approximation processes of integral type
(Springer, 2017) Agratini, Octavian; Aral, Ali; Deniz, Emre
The paper aims to study two classes of linear positive operators representing modifications of Picard and Gauss operators. The new operators reproduce both constants and a given exponential function. Approximation properties in polynomial weighted spaces are investigated and the speed of convergence is measured using a certain weighted modulus of smoothness. Also, the asymptotic behavior of the integral operators are established. Finally, aspects on generalized convexity are analyzed.