Uaday Singh | IIT Roorkee (original) (raw)
Papers by Uaday Singh
Applied mathematics and computation, Jan 1, 2007
In continuation of a recent work by Mittal [M.L. Mittal, On strong Nö rlund summability of Fourie... more In continuation of a recent work by Mittal [M.L. Mittal, On strong Nö rlund summability of Fourier series, J. Math. Anal. Appl. 314 (2006),75-84], the present authors obtain a sufficient condition for the summability ½N ; p ð1Þ n ; 2 of the conjugate Fourier series. In conjunction with the known Tauberian theorem on the strong Nö rlund summability, which was also considered earlier by Mittal [M.L. Mittal, A Tauberian theorem on strong Nö rlund summability, J. Indian Math. Soc. (N.S.) 44 (1980), 369-377], our result gives a sufficient condition for the summability [C, 1 , 2] of the conjugate Fourier series. Our main theorem generalizes the results given earlier by Prasad [G. Prasad, On Nö rlund Summability of Fourier Series, Ph.D. thesis, University of Roorkee, Roorkee, 1967] and Singh [U.N. Singh, On the strong summability of a Fourier series and its conjugate series, Proc. Nat. Inst. Sci. India Part A 13 (1947), 319-325].
Applied Mathematics and Computation, Jan 1, 2008
a b s t r a c t Let B n (x) denote the nth term of the conjugate series of a Fourier series of fu... more a b s t r a c t Let B n (x) denote the nth term of the conjugate series of a Fourier series of function f. Mohanty and Nanda [R. Mohanty, M. Nanda, On the behavior of Fourier coefficients, Proc. Am. Math. Soc. 5 (1954) 79-84] were the first to establish a result for C 1 -summability of the sequence {nB n (x)}. Varshney [O.P. Varshney, On a sequence of Fourier coefficients, Proc. Am. Math. Soc. 10 (1959) 790-795] improved it for the product summability H 1 Á C 1 , which was generalized by various investigators using different summability methods with different set of conditions. In this note, we extend the result of Mittal [M.L. Mittal, On the kTk Á C 1 summability of a sequence of Fourier coefficients, Bull. Cal. Math. Soc. 81 (1989) 25-31], which in turn generalizes the results of Prasad [K. Prasad, On the (N, p n ) Á C 1 summability of a sequence of Fourier coefficients, Indian J.
![Research paper thumbnail of Using infinite matrices to approximate functions of class Lip ([alpha], p) using trigonometric polynomials](https://attachments.academia-assets.com/51122604/thumbnails/1.jpg)
](Journal of mathematical …, Jan 1, 2007
The user has requested enhancement of the downloaded file. All in-text references underlined in b... more The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.
Applied mathematics and computation, Jan 1, 2007
In continuation of a recent work by Mittal [M.L. Mittal, On strong Nö rlund summability of Fourie... more In continuation of a recent work by Mittal [M.L. Mittal, On strong Nö rlund summability of Fourier series, J. Math. Anal. Appl. 314 (2006),75-84], the present authors obtain a sufficient condition for the summability ½N ; p ð1Þ n ; 2 of the conjugate Fourier series. In conjunction with the known Tauberian theorem on the strong Nö rlund summability, which was also considered earlier by Mittal [M.L. Mittal, A Tauberian theorem on strong Nö rlund summability, J. Indian Math. Soc. (N.S.) 44 (1980), 369-377], our result gives a sufficient condition for the summability [C, 1 , 2] of the conjugate Fourier series. Our main theorem generalizes the results given earlier by Prasad [G. Prasad, On Nö rlund Summability of Fourier Series, Ph.D. thesis, University of Roorkee, Roorkee, 1967] and Singh [U.N. Singh, On the strong summability of a Fourier series and its conjugate series, Proc. Nat. Inst. Sci. India Part A 13 (1947), 319-325].
Applied Mathematics and Computation, Jan 1, 2008
a b s t r a c t Let B n (x) denote the nth term of the conjugate series of a Fourier series of fu... more a b s t r a c t Let B n (x) denote the nth term of the conjugate series of a Fourier series of function f. Mohanty and Nanda [R. Mohanty, M. Nanda, On the behavior of Fourier coefficients, Proc. Am. Math. Soc. 5 (1954) 79-84] were the first to establish a result for C 1 -summability of the sequence {nB n (x)}. Varshney [O.P. Varshney, On a sequence of Fourier coefficients, Proc. Am. Math. Soc. 10 (1959) 790-795] improved it for the product summability H 1 Á C 1 , which was generalized by various investigators using different summability methods with different set of conditions. In this note, we extend the result of Mittal [M.L. Mittal, On the kTk Á C 1 summability of a sequence of Fourier coefficients, Bull. Cal. Math. Soc. 81 (1989) 25-31], which in turn generalizes the results of Prasad [K. Prasad, On the (N, p n ) Á C 1 summability of a sequence of Fourier coefficients, Indian J.
Journal of mathematical …, Jan 1, 2007
The user has requested enhancement of the downloaded file. All in-text references underlined in b... more The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.