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Das, G.
- An Estimate of the Rate of Convergence of Kλ-Means of Fourier Series of Functions of Bounded Variation
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Affiliations
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.
- J. Karamata, Theoremes sur la sommabiliti exponentielle et d’autres sommabilities s’y rattachant, Mathematica (Cluj), Vol.9(1935), 164–178.
- A. V. Lototsky,On a linear transformation of sequences and series ,Ped.Inst.Uch.Zap.Fiz-Mat.Nauki,Vol.4(1953), 61–91(Russian).
- G. Polya and G. Szeg¨o, Problems and Theorems in Analysis, Volume -I, Springer International student Edition.Narosa publishing House, NewDelhi 1979.
- Pratima Sadangi,Some Aspects of Approximation Theory, Ph.D Thesis Utkal University, Bhubaneswar, Orissa, India, year 2006.
- V. Vuckovic,The summability of Fourier series by Karamata methods, Math.Zeitschr. 89 (1965), 192–195.
- A. Zygmund,Trigonometric series , Vol.I and II combined, Cambridge University Press, New York, 1993.
- 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 :191 |
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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.- Some Inclusion Theorems for Norlund Methods
Abstract Views :155 |
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Authors
G. Das
1
Affiliations
1 G. M. College, Sambalpur, Orisaa, IN
1 G. M. College, Sambalpur, Orisaa, IN
Source
The Journal of the Indian Mathematical Society, Vol 35, No 1-4 (1971), Pagination: 241-248Abstract
The Oesaro method is 'imprisoned' between two special Norlund methods. In this note we determine Norlund methods which are imprisoned between Cesaro methods of two different orders. More specifically we consider Norlund methods which are weaker than (C, α) and stronger than (C, α + 1).- On a Theorem of Sunouchi
Abstract Views :144 |
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Authors
G. Das
1
Affiliations
1 Department of Mathematics, Sambalpur University, Burla, Sambalpur, Orissa, IN
1 Department of Mathematics, Sambalpur University, Burla, Sambalpur, Orissa, IN
Source
The Journal of the Indian Mathematical Society, Vol 38, No 1-4 (1974), Pagination: 155-174Abstract
This result is best possible in the sense that δ cannot be dropped.
The special case of this theorem in which α is an integer has been generalised as follows by introducing a general sequence of factors:
Theorem S'. [7], [11]. Let λn > 0 and non-decreasing and let α be a non-negative integer and let
Σ |σαn-σαn-1| = O(λm).
- Products of Norlund Method
Abstract Views :138 |
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Authors
G. Das
1
Affiliations
1 Department of Mathematics, University College of London, London, GB
1 Department of Mathematics, University College of London, London, GB
Source
The Journal of the Indian Mathematical Society, Vol 32, No 3-4 (1968), Pagination: 155-171Abstract
Given any sequence {qn} similarly defined as {Pn}, we shall denote by {N"nq} the (N, p) transform of the (N, q) transform of {Sn} and the correponding summability by (N, p) (N, q).- Some Theorems on Absolute Norlund Summability
Abstract Views :155 |
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Authors
G. Das
1
Affiliations
1 Bari-Cuttack, IN
1 Bari-Cuttack, IN
Source
The Journal of the Indian Mathematical Society, Vol 31, No 1 (1967), Pagination: 1-9Abstract
Let Σ an be a given infinite series, with {Sn} as the sequence of nth partial sums. Let {pn} be a sequence of constants, real or complex, and we write
Pn = P0 + P1 + .... + Pn; P-1 = P-1 = 0.
The sequence-to-sequence transformation.
- On Functional Methods
Abstract Views :150 |
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Authors
G. Das
1
Affiliations
1 Department of Mathematics, University College, London Gower Street, London, GB
1 Department of Mathematics, University College, London Gower Street, London, GB
Source
The Journal of the Indian Mathematical Society, Vol 31, No 2 (1967), Pagination: 81-93Abstract
Let S be the class of all complex valued functions A{t) of a real variable t defined for all positive t and bounded and measurable in every finite interval (0, c), c > 0.- Fixed Points on Unit Interval Using Estfinite Matrices
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Authors
G. Das
1,
J. P. Debata
2
Affiliations
1 Department of Mathematics, Utkal University, Bhubaneswar-751004, IN
2 Department of Mathematics, Dhenkanal Mahila Mabavidyalaya, Dhenkanal 759 001, IN
1 Department of Mathematics, Utkal University, Bhubaneswar-751004, IN
2 Department of Mathematics, Dhenkanal Mahila Mabavidyalaya, Dhenkanal 759 001, IN
Source
The Journal of the Indian Mathematical Society, Vol 53, No 1-4 (1988), Pagination: 167-176Abstract
Let J be a continuous self-map on [0, 1]. Fixed points of T can be approached by means of iterative methods.- Some Generalisation of Strong and Absolute almost Convergence
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Authors
Affiliations
1 P.G. Dept. of Mathematics, Utkal University, Bhubaneswar—751004, IN
2 Dept. of Mathematics, Regional College of Education, Bhubaneswar—751007, IN
1 P.G. Dept. of Mathematics, Utkal University, Bhubaneswar—751004, IN
2 Dept. of Mathematics, Regional College of Education, Bhubaneswar—751007, IN
Source
The Journal of the Indian Mathematical Society, Vol 60, No 1-4 (1994), Pagination: 225-246Abstract
Let l∞ be set of all bounded sequences x = (xn) with the norm
||x|| = sup |xn|.
Given an infinite series Σ an which we will denote by a, let
xn = a0 + a1 + ......... + an (1.1)
We will suppose throughout that a and x are connected by the relation (1.1).