Higher order iterates of Szasz-Mirakyan-Baskakov operators (original) (raw)

Approximation by a generalization of Szasz-Mirakjan type operators

Studia Universitatis Babes-Bolyai Matematica, 2020

In the present paper we propose a new generalization of Sz\'{a}sz-Mirakjan-type operators. We discuss their weighted convergence and rate of convergence via weighted modulus of continuity. We also give an asymptotic estimate through Voronovskaja type result for these operators.

Simultaneous Approximation for Generalized Baskakov-Durrmeyer-Type Operators

Mediterranean Journal of Mathematics, 2007

The present paper deals with the study of a Durrmeyer-type integral modification of certain modified Baskakov operators. Here we study simultaneous approximation properties for these operators by using the iterative combinations. We obtain an asymptotic formula and an error estimation in terms of higher order modulus of continuity for these operators.

Approximation by Kantorovich form of modified Szász–Mirakyan operators

Applied Mathematics and Computation, 2018

In the present article, we consider the Kantorovich type generalized Szász-Mirakyan operators based on Jain and Pethe operators [32]. We study local approximation results in terms of classical modulus of continuity as well as Ditzian-Totik moduli of smoothness. Further we establish the rate of convergence in class of absolutely continuous functions having a derivative coinciding a.e. with a function of bounded variation.

Approximation by k-th order modifications of Szász—Mirakyan operators

Studia Scientiarum Mathematicarum Hungarica, 2016

In this paper, we study the k-th order Kantorovich type modication of Szász—Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szász—Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.

Approximation Properties of Generalized Szász-Type Operators

Acta Mathematica Vietnamica, 2018

In the present paper, we study some approximation properties of the generalized Szász type operators introduced by V. Miheşan (Creat. Math. Inf. 17:466-472, 2008). We present a quantitative Voronovskaya-type theorem, local approximation theorem by means of second-order modulus of continuity and weighted approximation for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained.

Simultaneous approximation by a new sequence of Szãsz-beta type operators

Revista de la Unión Matemática …, 2009

In this paper, we study some direct results in simultaneous approximation for a new sequence of linear positive operators Mn(f (t); x) of Szãsz-Beta type operators. First, we establish the basic pointwise convergence theorem and then proceed to discuss the Voronovaskaja-type asymptotic formula. Finally, we obtain an error estimate in terms of modulus of continuity of the function being approximated.

On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics

In the present paper, we introduce certain modi…cation of Szász-Mirakyan-Kantorovich-type operators in polynomial weighted spaces of continuous functions of two variables. Then we research some approximation properties of these operators. We give some inequalities for the operators by means of the weighted modulus of continuity and also obtain a Voronovskaya-type theorem. Furthermore, in the paper we show that our operators give better degree of approximation of functions belonging to weighted spaces than classical Szász-Mirakyan operators.