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2011•Lobachevskii Journal of MathematicsRequires access

Generalized Szász Durrmeyer operators

Ali̇ Aral, Vijay Gupta

Open publisher page 12 citations

Abstract

In this paper, we introduce and study a new sequence of positive linear operators acting on the spaces of continuous function on positive semi-axis. These operators are defined by means of the q -integral, which generalize the Szász Durrmeyer operators. We study their approximation property by presenting a direct approximation theorem on polynomial weighted spaces and the rate of convergence by means of weighted modulus of continuity. Also, we establish an asymptotic formula with respect to weighted norm.

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What this paper is about

In this paper, we introduce and study a new sequence of positive linear operators acting on the spaces of continuous function on positive semi-axis. These operators are defined by means of the q -integral, which generalize the Szász Durrmeyer operators. We study their approximation property by presenting a direct approximation theorem on polynomial weighted spaces and the rate of convergence by means of weighted modulus of continuity. Also, we establish an asymptotic formula with respect to weighted norm.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we introduce and study a new sequence of positive linear operators acting on the spaces of continuous function on positive semi-axis. These operators are defined by means of the q -integral, which generalize the Szász Durrmeyer operators. We study their approximation property by presenting a direct approximation theorem on polynomial weighted spaces and the rate of convergence by means of weighted modulus of continuity. Also, we establish an asymptotic formula with respect to weighted norm.

Key concepts: Mathematics, Modulus of continuity, Linear operators, Operator norm, Operator theory, Rate of convergence, Polynomial, Sequence (biology)

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