q-Gamma Type Operators for Approximating Functions of a Polynomial Growth

Purshottam Narain Agrawal; Behar Baxhaku; Ruchi Chauhan

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q-Gamma Type Operators for Approximating Functions of a Polynomial Growth

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We investigate the rate of convergence of the operators introduced by Singh et al. (Linear Multilinear Algebra, 2022.) for functions of a polynomial growth. By using Steklov means, we obtain an estimate of error for these operators in terms of the modulus of continuity of order two. We derive an asymptotic theorem of Voronovskaja type and its quantitative form. Further, we modify these operators to examine the approximation of smooth functions in the above polynomial weighted space, i.e. a space of functions under a norm that involves multiplication by a polynomial function referred to as the weight and show that we achieve better approximation. We also discuss the convergence in the Lipschitz space and a Voronovskaja type asymptotic result.

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来源
《Iranian Journal of Science》 |2023年第4期|1367-1377|共11页
作者
Purshottam Narain Agrawal; Behar Baxhaku; Ruchi Chauhan;
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作者单位

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India;

Department of Mathematics, University of Prishtina 'Hasan Prishtina', Prishtina, Kosovo;

Department of Mathematics, K. G. K. (PG) College, Moradabad 244001, India;

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正文语种英语
中图分类自然科学理论与方法论;
关键词
Gamma type operators; Modulus of continuity; Polynomial weighted space; Rate of convergence; Steklov means; Voronovskaja type theorem;

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q-Gamma Type Operators for Approximating Functions of a Polynomial Growth

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