Abstract
In this paper, we have studied an estimate of the rate of convergence of Fourier series in the generalized Hölder metric \(H_{L_{r}}^{(\omega )}\) space by using deferred Nörlund mean and established some new results. Our results are more advanced that generalize and unify many other results available in the literature.
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References
Agnew, R.P.: On deferred Cesàro means. Ann. Math. 33, 413–421 (1932)
Das, G., Ghosh, T., Ray, B.K.: Degree of approximation of function by their Fourier series in the generalized Hölder metric. Proc. Indian Acad. Sci. Math. Sci. 106, 139–153 (1996)
Das, G., Nath, A., Ray, B.K.: An estimate of the rate of convergence of Fourier series in the generalized Hölder metric. Anal. Appl. 5, 43–60 (2002)
Deǧer, U., Küçükaslan, M.: A generalization of deferred Cesàro means and some of their applications, J. Inequal. Appl., (2015), Article ID-14, 1–16
Leindler, L.: Generalization of Prössdorf’s theorems. Stud. Sci. Math. Hungar. 14, 431–439 (1979)
Nayak, L., Das, G., Ray, B.K.: An estimate of the rate of convergence of Fourier series in the generalized Hölder metric by Deferred Cesàro mean. J. Math. Anal. Appl. 420, 563–575 (2014)
Zygmund, A.: Trigonometric series, volumes I and II combined, 2nd edn. Cambridge University Press, New York (1993)
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Pradhan, T., Jena, B.B., Paikray, S.K. et al. On approximation of the rate of convergence of Fourier series in the generalized Hölder metric by Deferred Nörlund mean. Afr. Mat. 30, 1119–1131 (2019). https://doi.org/10.1007/s13370-019-00706-y
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DOI: https://doi.org/10.1007/s13370-019-00706-y