Approximation of Fourier-Laguerre expansion based on a new product deferred summability means. (English) Zbl 1524.40032
Summary: Summability theory in combination with Fourier analysis is found to be very useful and fruitful subject of research as they can together fulfil several needs to deal with various phenomena occur in engineering and technology. The deferred summability means has remarkably attracted a large number of researchers due mainly to the fact that it is well-behaved to preserve uniform convergence and mean-square convergence of sequences of functions. In the present investigation, we have studied the notion (presumably new) of deferred Nörlund and deferred Euler product summability means. We then make use of this mean to obtain the degree of approximation of Fourier-Laguerre series of a function at \(x=0\). Moreover, to show the effectiveness of our study we deduce one corollary as the generalization of our main result. Finally, we have proposed some future works in the conclusion section of our study.
MSC:
| 40G05 | Cesàro, Euler, Nörlund and Hausdorff methods |
| 41A25 | Rate of convergence, degree of approximation |
| 42B05 | Fourier series and coefficients in several variables |
| 42B08 | Summability in several variables |
Keywords:
degree of approximation; Fourier-Laguerre expansion; deferred Euler summability mean; deferred Nörlund summability mean; deferred Nörlund and Euler product summability methodReferences:
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