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Ray, B. K.
- An Estimate of the Rate of Convergence of Kλ-Means of Fourier Series of Functions of Bounded Variation
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1 Deptartment of Mathematics, College of Basic Science and Humanities, OUAT Bhubaneswar - 751 030, IN
2 177, Dharma Vihar, Khandagiri, Bhubaneswa - 751030, IN
3 Plot.No-102, Saheed Nagar, Bhubaneswar - 751 007, IN
1 Deptartment of Mathematics, College of Basic Science and Humanities, OUAT Bhubaneswar - 751 030, IN
2 177, Dharma Vihar, Khandagiri, Bhubaneswa - 751030, IN
3 Plot.No-102, Saheed Nagar, Bhubaneswar - 751 007, IN
Source
The Journal of the Indian Mathematical Society, Vol 81, No 3-4 (2014), Pagination: 205-218Abstract
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
- R. Bojanic, An estimate of the rate of convergence of Fourier series of functions of bounded variation, Inst. Math. (Beograd), (N. S.) 26 (1979), 57–60 . [2] R. Bojanic and S. M. Mazhar,An estimate of the rate of convergence of Ces´aro means of Fourier series of functions of bounded variation, Proc. of the conference on Mathematical Analysis and its applications, Kuwait(1985), Oxford Pergamon Press, 17–22.
- R. Bojanic and S. M. Mazhar, An estimate of the rate of convergence of the N¨orlundVoronoi means of the Fourier series of functions of bounded variation, Approx. Theory III,Academic Press (1980), 243–248.
- G. Das, Anasuya Nath and B. K. Ray, An estimate of the rate of convergence of Fourier series in the generalised H¨older metric,Analysis and Applications, (2002), Narosa publishing House, New Delhi, India, 43–60.
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- Degree of Approximation of Fourier Series of Functions in Besov Space by Deferred Cesaro Mean
Abstract Views :304 |
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Authors
Affiliations
1 School of Applied Sciences, KIIT University, Bhubaneswar-751024, IN
2 177, Dharma Vihar, Khandagiri, Bhubaneswar-751030, IN
3 Plot.No-102, Saheed Nagar, Bhubaneswar-751007, IN
1 School of Applied Sciences, KIIT University, Bhubaneswar-751024, IN
2 177, Dharma Vihar, Khandagiri, Bhubaneswar-751030, IN
3 Plot.No-102, Saheed Nagar, Bhubaneswar-751007, IN
Source
The Journal of the Indian Mathematical Society, Vol 83, No 1-2 (2016), Pagination: 161-179.Abstract
In the present article, we study the degree of approximation of Fourier series of functions by deferred Cesaro mean in Besov space which is a generalization of H(α, p) space.Keywords
Fourier Series, Besov Space, Deferred Cesaro Mean, Delayed Arithmetic Mean.References
- R. P. Agnew, On deferred Cesaro means, Ann. Math., 33, (1932), 413-421.
- G. Alexits, Convergence problems of othogonal series, Pergamn Press, Newyork, 1961.
- P. Chandra, On the generalized Fejer means in the metric of Holder space, Math. Nachar, 109, (1982), 39-45.
- P. Chandra and R. N. Mohapatra, Degree of approximation of functions in the Holder metric, Acta Math. Hungar., 41, (1983), 67-76.
- G. Das, T. Ghosh and B. K. Ray, Degree of approximation of function by their Fourier series in the generalized Holder metric, Proc. Indian Acad. Sci(Math. Sci.), 106, (1996), 139-153.
- A. Devore Ronald and G. Lorentz, Constructive approximation, Springer Verlag, Berlin Neidelberg, New York, 1993.
- H. Mohanty, Some aspects of measure of approximations, Ph.D Dissertation, 2012.
- L. Nayak, G. Das and B. K. Ray, An estimate of the rate of convergence of Fourier series in the generalized Holder metric by Deferred Cesaro mean, J. Math. Anal. Appl. 420, (2014), 563-575.
- S. Prossdorf, zur Konvergenz der Fourir reithen Holder stetiger Funktionen, Math. Nachr., 69, (1975), 7-14.
- P. Wojtaszczyk, A Mathematical introduction to Wavelets, London Math. Soc. stuents texts, 37, Cambridge University Press, New York, 1997.
- A. Zygmund, Smooth functions, Duke Math. J. 12, (1945), 47-56.
- A. Zygmund, Trigonometric Series, Second Edition, Volumes I and II combined, Cambridge University Press, New York, 1993.
- Almost Convergence of Conjugate Series
Abstract Views :192 |
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Authors
Affiliations
1 Institute of Mathematics and Applications Andharua, Bhubaneswar, Orissa, IN
1 Institute of Mathematics and Applications Andharua, Bhubaneswar, Orissa, IN
Source
The Journal of the Indian Mathematical Society, Vol 77, No 1-4 (2010), Pagination: 37-45Abstract
The object of the paper is to obtain certain criteria for the existence of unique Banach limit of conjugate series of a Fourier Series.Keywords
Cayley–Lipschitz Transformations, Orthogonal and Clifford Groups over Rings, Quasi-Inverses.- On the Summ Ability (R, log n, 1) of a Sequence Associated with Fourier Coefficients
Abstract Views :148 |
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Authors
Affiliations
1 Department of Mathematics, J.K.B.K. College, Cuttack-7, Orissa, IN
1 Department of Mathematics, J.K.B.K. College, Cuttack-7, Orissa, IN
Source
The Journal of the Indian Mathematical Society, Vol 39, No 1-4 (1975), Pagination: 309-313Abstract
Let Σan be an infinite series and Sn be its nth partial sum. If the sequence Σan (or the sequence Sn) is said to be summable by logarithmic mean or summable (R, logn, 1) to S.- On the Absolute Summability of Fourier Integral by Abel-Type Method
Abstract Views :182 |
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Authors
Affiliations
1 Department of Mathematics, J.K.B.K. College, Cuttack 753007, Orissa, IN
2 Department of Mathematics, Ravenshaw College, Cuttack 753003, Orissa, IN
1 Department of Mathematics, J.K.B.K. College, Cuttack 753007, Orissa, IN
2 Department of Mathematics, Ravenshaw College, Cuttack 753003, Orissa, IN