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An Estimate of the Rate of Convergence of Kλ-Means of Fourier Series of Functions of Bounded Variation


Affiliations
1 Deptartment of Mathematics, College of Basic Science and Humanities, OUAT Bhubaneswar - 751 030, India
2 177, Dharma Vihar, Khandagiri, Bhubaneswa - 751030, India
3 Plot.No-102, Saheed Nagar, Bhubaneswar - 751 007, India
     

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Bojanic first obtained an estimate of the rate of convergence of Fourier series of functions of bounded variation. Later on Bojanic and Mazhar studied the rate of convergence of Cesaro means and Norlund means of Fourier series of functions of bounded variation. In the present work we obtain an estimate for the rate of convergence of Kλ-means of Fourier series of functions of bounded variation. Our result asserts that rate of convergence of Kλ-means of Fourier series at a point can be ensured by a local condition where as the earlier estimates obtained by Bojanic and Mazhar for Cesaro and Norlund means of Fourier series are all under non-local conditions.
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  • An Estimate of the Rate of Convergence of Kλ-Means of Fourier Series of Functions of Bounded Variation

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Authors

Sanghamitra Beuria
Deptartment of Mathematics, College of Basic Science and Humanities, OUAT Bhubaneswar - 751 030, India
G. Das
177, Dharma Vihar, Khandagiri, Bhubaneswa - 751030, India
B. K. Ray
Plot.No-102, Saheed Nagar, Bhubaneswar - 751 007, India

Abstract


Bojanic first obtained an estimate of the rate of convergence of Fourier series of functions of bounded variation. Later on Bojanic and Mazhar studied the rate of convergence of Cesaro means and Norlund means of Fourier series of functions of bounded variation. In the present work we obtain an estimate for the rate of convergence of Kλ-means of Fourier series of functions of bounded variation. Our result asserts that rate of convergence of Kλ-means of Fourier series at a point can be ensured by a local condition where as the earlier estimates obtained by Bojanic and Mazhar for Cesaro and Norlund means of Fourier series are all under non-local conditions.

References