Approximation by Double Deferred Nörlund Means of Double Fourier Series for Lipschitz Functions

Şeyda Sezgek; İlhan Dağadur

doi:10.17776/csj.439832

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Approximation by Double Deferred Nörlund Means of Double Fourier Series for Lipschitz Functions

Abstract

In this paper, the concept of Double Deferred Nörlund means is defined and some important results are obtained. Particularly, we investigate the rate of uniform approximation by Double Deferred Nörlund means of the rectangular partial sums of the double Fourier series of a function belong to on the two dimensional region . We also obtain the rate of uniform approximation by Double Deferred Cesáro means.

Keywords

Functions of bounded variation,Ostrowski type inequalities,Riemann-Stieltjes integrals

References

[1] Armitage D. H., Maddox I. J., A new type of Cesáro mean. Analysis 9 (1989) 195-206.
[2] Başarır M., Sonalcan O., On some double sequence spaces. J. Indiana cad. math. 21 (1999) 193-200.
[3] Bromwich T. J., An introduction to the theory of infinite series. Macmillan and co. Ltd., New York (1965).
[4] Dağadur İ., Sezgek Ş. Deferred Cesàro mean and deferred statistical convergence of double sequences. J. İneq. And special func. 7-4 (2016) 118-136.
[5] Goffman C., Petersen G. M., Submethods of regular matrix summability methods. Canad. J. Math. 8 (1956) 40-46.
[6] Hamilton H. J., Transformations of double series. Bull. Amer. Math. Soc. 42 (1936) 275-283.
[7] Hardy G. H., On the convergence of certain multiple series. Proc. London math. Soc. 2-1 (1904) 124-128.
[8] Lal S., On the degree of approximation of functions belonging to the weighted -class by (C,1)(E,1) means, Tamkang J. Math. 30-1(1999) 47-52.

[9] Lal S., On the degree of approximation of conjugate of a function belonging to the weighted -class by matrix summability means of conjugate series of a fourier series, Tamkang J. Math, 31-4(2000) 279-288.
[10] McFadden L., Absolute Nörlund Summability, Duke Math. J. 9(1942) 168-207.
[11] Mittal M. L., Singh U., Mishra V. N., Approximation of signals (functions) belonging to the weighted -class by Nörlund means. Varahmihir J. Math. Sci. 6-1(2006) 383-392.
[12] Moore C. N., Summable series and convergence factors. Amer. Math. Soc. Colloq. Publ. 22 (1938).
[13] Móricz F., Rhoades B. E., Approximation by Nörlund means of double Fourier series for Lipschitz functions, J. of App. Theory 50 (1987) 341-358.
[14] Móricz F., Extension of the spaces and from single to double sequence. Acta math. Hungarica 57 (1991) 129-136.
[15] Osikiewicz J. A., Equivalence results for Cesàro submethods. Analysis 20 (2000) 35-43.
[16] Patterson R. F., Analogues of some fundamental theorems of summability theory. Int. J. Math. Math. Sci. 23 (2000) 1-9.
[17] Qureshi K., On the degree of approximation of functions belonging to the weighted -class, Indian J. Pure Appl. Math. 13(1982) 471-475.
[18] Robison G. M., Divergent double sequences and series. Amer. Math. Soc. 28 (1926) 50-73.
[19] Tripathy B. C., Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex spaces. Soochow J. Math. 30 (2004) 431-446.
[20] Ünver M., Inclusion results for four dimensional Cesàro submethods. Stud. Univ. Babeş Bolyai vmath. 58-1 (2013) 43-54.
[21] Yıldırım M., Karakuş F., On the degree of approximation to a function belonging to the weighted -class by means, East Asian Mathematical J. 20(2004) 1-9.
[22] Yıldırım M., Karakuş F., The almost (C,1)(E,1) summability of a fourier series and its conjugate series, Bull. Cal. Math. Soc. 98-4(2006) 285-294.
[23] Yıldırım M., Karakuş F., On summability of the sequence . E-Journal of New World Scienses Academy, 4-4(2009) 117-123.
[24] Zeltser M., On conservative and coercive SM-methods. Proc. Estonian acad. Sci. Phys. Math. 50-2 (2001) 76-85.
[25] Zeltser M., Investigation of double sequence spaces by soft and hard analytical methods. Diss. Math. Univ. Tartu. 25 Tartu Univ. Pres. Univ. of Tartu, faculty of mathematics and computer science, Tartu (2001).
[26] Zygmund A., Trigonometric series. J. Cambridge Univ. pres, Cambridge (1959).

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Şeyda Sezgek
Türkiye

İlhan Dağadur ^*
Türkiye

Publication Date

September 30, 2018

Submission Date

July 2, 2018

Acceptance Date

September 24, 2018

Published in Issue

Year 2018 Volume: 39 Number: 3

DOI

https://doi.org/10.17776/csj.439832

IZ

https://izlik.org/JA26RC57XW

Cite

RIS / Bibtex

APA

Sezgek, Ş., & Dağadur, İ. (2018). Approximation by Double Deferred Nörlund Means of Double Fourier Series for Lipschitz Functions. Cumhuriyet Science Journal, 39(3), 581-596. https://doi.org/10.17776/csj.439832

Cited By

Applications of the deferred generalized de la Vallee Poussin means in approximation of continuous functions

Studia Universitatis Babes-Bolyai Matematica

https://doi.org/10.24193/subbmath.2022.4.12

Approximation by Double Deferred Nörlund Means of Double Fourier Series for Lipschitz Functions

Approximation by Double Deferred Nörlund Means of Double Fourier Series for Lipschitz Functions

Abstract

Keywords

Lipschitz Fonksiyonları için Çift İndisli Fourier Serilerinin Double Deferred Nörlund Ortalamasıyla Yaklaşım

Öz

Anahtar Kelimeler

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

Cited By

Applications of the deferred generalized de la Vallee Poussin means in approximation of continuous functions