PRODUCT (N, PN) (C, 1) SUMMABILITY OF A SEQUENCE OF FOURIER COEFFICIENTS

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MISHRA VISHNU NARAYAN; KHATRI KEJAL; MISHRA LAKSHMI NARAYAN

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Journal: MATHEMATICAL SCIENCES Year:2012 | Volume:6 | Issue:- Page(s): 1-5

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Title

PRODUCT (N, PN) (C, 1) SUMMABILITY OF A SEQUENCE OF FOURIER COEFFICIENTS

Author(s)

MISHRA VISHNU NARAYAN | KHATRI KEJAL | MISHRA LAKSHMI NARAYAN | Issue Writer Certificate

Keywords

CONJUGATE FOURIER SERIES

1) SUMMABILITY

PN) SUMMABILITY AND PRODUCT

PN) (C

1) SUMMABILITY

Abstract

Purpose: The purpose of the present paper is to study the product (N, pn) (C, 1) summability of a sequence of Fourier coefficients which extends a theorem of Prasad.Methods: We use Np. C1 summability methods with dropping monotonicity on the generating sequence {pn−k} (that is, by weakening the conditions on the filter, we improve the quality of digital filter).Results: Let Bn(x) denote the nth term of conjugate series of a Fourier series. Mohanty and Nanda were the first to establish a result for C1 summability of the sequence {n Bn(x)}. Varshney improved the result for H1. C1 summability which was generalized by various investigators using different summability methods with different sets of conditions. In this paper, we extend a result of Prasad by dropping the monotonicity on the sequence {pn−k}.Conclusions: Various results pertaining to the C1 and H1. C1 summabilities of the sequence {n B n (x)} have been reviewed and the condition of monotonicity on the means generating the sequence {pn−k} has been relaxed. Moreover, a proper set of conditions have been discussed to rectify the errors pointed out in Remark 3.2 (1) and (2).

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References

APPROXIMATION OF FUNCTIONS BELONGING TO LIP (XI (T),R) CLASS BY (N,P N )(E,Q) SUMMABILITY OF CONJUGATE SERIES OF FOURIER SERIES

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APA: Copy

MISHRA, VISHNU NARAYAN, KHATRI, KEJAL, & MISHRA, LAKSHMI NARAYAN. (2012). PRODUCT (N, P_N) (C, 1) SUMMABILITY OF A SEQUENCE OF FOURIER COEFFICIENTS. MATHEMATICAL SCIENCES, 6(-), 1-5. SID. https://sid.ir/paper/322606/en

Vancouver: Copy

MISHRA VISHNU NARAYAN, KHATRI KEJAL, MISHRA LAKSHMI NARAYAN. PRODUCT (N, P_N) (C, 1) SUMMABILITY OF A SEQUENCE OF FOURIER COEFFICIENTS. MATHEMATICAL SCIENCES[Internet]. 2012;6(-):1-5. Available from: https://sid.ir/paper/322606/en

IEEE: Copy

VISHNU NARAYAN MISHRA, KEJAL KHATRI, and LAKSHMI NARAYAN MISHRA, “PRODUCT (N, P_N) (C, 1) SUMMABILITY OF A SEQUENCE OF FOURIER COEFFICIENTS,” MATHEMATICAL SCIENCES, vol. 6, no. -, pp. 1–5, 2012, [Online]. Available: https://sid.ir/paper/322606/en

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