On The Approximation Of Conjugate Of Functions Belonging To The Generalized Lipschitz Class By Euler-matrix Product Summability Method Of Conjugate Series Of Fourier Series

Jitendra Kumar Kushwaha, Krishna Kumar

Abstract


In this paper, a new theorem on the approximation of conjugate of functions belonging to the generalized Lipschitz class $Lip\left(\xi(t),p \right) $ by Euler-Matrix product summability method of conjugate series of Fourier series has been obtained.

Keywords


generalized Lipschitz class, conjugate series of Fourier series, product summability method, Euler mean, matrix mean.

Full Text:

PDF

References


P. Chandra, Trigonometric approximation of functions in norm, J. Math. Anal. Appl., 275, No 1 (2002), 13-26.

G. H. Hardy, Divergent Series, American Mathematical Society, (2000).

A. S. B. Holland and B. N. Sahney, On the degree of approximation by (E, q) means, Studia Sci. Math. Hunger, 11 (1976), 431-435.

J. K. Kushwaha, On the approximation of conjugate function by almost triangular matrix summability means, Int. J. of Management Tech. and Engi., 9, No 3 (2019), 4382-4389; DOI: 16.10089.IJMTE.2019.V913.19.27979.

S. Lal and J. K. Kushwaha, Degree of approximation of Lipschitz function by product summability methods, International Mathematical Forum, 4, No 43 (2009), 2101-2107.

S. Lal and J. K. Kushwaha, Approximation of conjugate of functions belonging to generalized Lipschitz class by lower triangular matrix means, Int. Journal of Math. Analysis, 3, No 21 (2009), 1031-1041.

K. Qureshi, On the degree of approximation of a function belonging to the weighted class, Indian Jour. of Pure and Appl. Math, 4, No 13 (1982), 471-475.

E. C. Titchmarsh, The Theory of Functions, Oxford University Press , (1939).

S. K. Tiwary and U. Upadhyay, Degree of approximation of functions belonging to the generalized Lipschitz class by product means of its Fourier series, Ultra Scientist, 3, No 25 (2013), 411-416.

O. Töeplitz, Über die Lineare mittelbi-dungen Prace, Mat. Fiz., No 22 (1911), 113-119.

A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, (1959).

C.K.Chui. An introduction to Wavelets (wavelets analysis and it's application), Vol.1, Academic Press, USA, 1992.

Jitendra Kumar Kushwaha, On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series, The Scientific World Journal, Vol. 2013, Article Id 508026.

Sandeep Kumar Tiwari and Uttam Upadhyay, Degree of Approximation of Function Belonging to class by (E,q) A-Product Means of its Fourier series, IJM Archive- 4(8), 2013, 266-272.

Xhevat Z. Krasniqi, On the Degree of Approximation of Functions Belonging to the Lipschitz Class by Means, Khayyam J. Math, 1(2015), no.2 243-252.

Jitendra Kumar Kushwaha, Approximation of functions by (C,2)(E,1) product summability method of Fourier series. Ratio Mathematica, Vol 38, 2020, pp. 341-348.




DOI: http://dx.doi.org/10.23755/rm.v42i0.788

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Jitendra Kumar Kushwaha, krishna Kumar

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.