scholarly journals Mean summability methods for Laguerre series

1990 ◽  
Vol 322 (2) ◽  
pp. 671-690 ◽  
Author(s):  
Krzysztof Stempak
Keyword(s):  
Laguerre Series ◽  
Summability Methods

scholarly journals Error Estimation of Functions by Fourier-Laguerre Polynomials Using Matrix-Euler Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
M. L. Mittal ◽  
Mradul Veer Singh
Keyword(s):  
Error Estimation ◽  
Laguerre Polynomials ◽  
Degree Of Approximation ◽  
Continuity Condition ◽  
Frontier Point ◽  
Laguerre Series ◽  
Summability Methods ◽  
The Individual ◽  
Euler Operators ◽  
Cesàro Matrix

Various investigators have studied the degree of approximation of a function using different summability (Cesáro means of order α: Cα, Euler Eq, and Nörlund Np) means of its Fourier-Laguerre series at the point x=0 after replacing the continuity condition in Szegö theorem by much lighter conditions. The product summability methods are more powerful than the individual summability methods and thus give an approximation for wider class of functions than the individual methods. This has motivated us to investigate the error estimation of a function by (T·Eq)-transform of its Fourier-Laguerre series at frontier point x=0, where T is a general lower triangular regular matrix. A particular case, when T is a Cesáro matrix of order 1, that is, C1, has also been discussed as a corollary of main result.

scholarly journals Pointwise Convergence of Fourier-Laguerre Series of Integrable Functions

2018 ◽  
Vol 60 (1) ◽  
pp. 93-101
Author(s):  
Włodzimierz Łenski ◽  
Bogdan Szal
Keyword(s):  
Pointwise Convergence ◽  
Strong Summability ◽  
Partial Sums ◽  
Laguerre Series ◽  
Summability Methods ◽  
Integrable Functions

Abstract We extend and improve the some results of Xh. Z. Krasniqi [Int. J. of Anal. and Appl. Vol. 1, 33-39 (2013)], M. L. Mittal and M. V. Singh [Operators, Int. J. of Analysis, Vol. 2015, Article ID 478345, 4 pages] and from many other papers on summability of Fourier-Laguerre series to strong summability proving the estimate of the deviation of the partial sums from considered functions. There also is a remark on summability methods used in cited papers.

scholarly journals On Dirichlet convolution method

1998 ◽  
Vol 21 (3) ◽  
pp. 607-611
Author(s):  
Indulata Sukla
Keyword(s):  
Summability Methods ◽  
Dirichlet Convolution ◽  
Convolution Method

In this paper we have proved limitation theorem for(D,h(n))summability methods and have shown that it is best possible.

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