Degree of Approximation by the $(T.E^1)$ Means of Conjugate Series of Fourier Series in the Hölder Metric

	Degree of Approximation by the $(T.E^1)$ Means of Conjugate Series of Fourier Series in the Hölder Metric
Iranian Journal of Science
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 مهر 1394
نوع مقاله: Regular Paper
شناسه دیجیتال (DOI): 10.22099/ijsts.2015.3225
نویسندگان
Kejal Khatri؛ Vishnu Narayan Mishra^*
Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat - 395 007 (Gujarat), India
چکیده
We compute the degree of approximation of functions f^~ in Hw a new Banach space using $(T.E^1)$ summability means of conjugate series of Fourier series. In this paper, we extend the results of Singh and Mahajan [T. Singh and P. Mahajan, Error bound of periodic signals in the H"{o}lder metric, Int. J. Math. Math. Sci. Volume 2008 (2008), Article ID 495075, 9 pages] which in turn generalizes the result of Lal and Yadav [S. Lal and K. N. S. Yadav, On degree of approximation of function belonging to the Lipschitz class by $(C,1)(E,1)$ means of its Fourier series, Bull. Cal. Math. Soc. Vol. 93 (2001) 191 -196]. Some corollaries have also been deduced from our main theorem and particular cases.
کلیدواژه‌ها
Conjugate series of Fourier series؛ Degree of approximation؛ Hölder Metric؛ Matrix summability؛ product summability

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