Research Article
Year 2018,
, 581 - 596, 30.09.2018
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.
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).
Lipschitz Fonksiyonları için Çift İndisli Fourier Serilerinin Double Deferred Nörlund Ortalamasıyla Yaklaşım
Abstract
Bu çalışmada, Double Deferred Nörlund ortalaması kavramı tanımlandı ve
bazı önemli sonuçlar elde edildi. Özellikle, iki boyutlu torus bölgesinde sınıfına ait fonksiyonunun çift
indisli Fourier serisinin dikdörtgensel kısmi toplamlarının çift indisli
Deferred Nörlund ortalamasıyla düzgün yaklaşım oranını araştırıyoruz. Ayrıca;
Double Deferred Cesáro ortalaması yardımı ile düzgün yaklaşım oranı elde
ediyoruz.
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).
There are 26 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | September 30, 2018 |
| Submission Date | July 2, 2018 |
| Acceptance Date | September 24, 2018 |
| Published in Issue | Year 2018 |