Approximation of signals of class Lip(α,p) by linear operators

Mittal, Madan Lal; Rhoades, Β. E.; Sonker, Smita; Singh, Uaday

doi:10.1016/j.amc.2010.10.051

Cited by 24 publications

(12 citation statements)

References 8 publications

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“…In this paper, we extend the theorem on lower triangular matrices of Mittal and Singh [20] in which they have extended two theorems of Leindler [9] using C λmethod obtained by deleting a set of rows from Cesàro matrix C 1 . Our theorem also generalize the theorem of Mittal et al [19] to T -matrix which in turn generalizes the results of Quade [27]. Here, we determine the degree of approximation which depends on strictly increasing sequence of positive integers i.e., the error of approximation is of order (λ) −α .…”

Section: Resultssupporting

confidence: 65%

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Approximation of signals (functions) of Lip(α, p), (p > 1)-class by trigonometric polynomials

Khatri¹,

Mishra²

2018

Publ Inst Math (Belgr)

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Given a function f in the class Lip(α, p) (0 < α 1, p 1), Mittal and Singh (2014) approximated such an f by using trigonometric polynomials, which are the n th terms of either certain Riesz mean or Nörlund mean transforms of the Fourier series representation for f. They showed that the degree of approximation is O((λ(n)) −α) and extended two theorems of Leindler (2005) where he had weakened the conditions on {pn} given by Chandra (2002) to more general classes of triangular matrix methods. We obtain the same degree of approximation for a more general class of lower triangular matrices.

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Section: Resultssupporting

confidence: 65%

“…Theorem 2.1. [19]. Let f ∈ Lip(α, p), and let T = (a n,k ) be an infinite regular triangular matrix.…”

Section: Known Resultsmentioning

confidence: 99%

Approximation of signals (functions) of Lip(α, p), (p > 1)-class by trigonometric polynomials

Khatri¹,

Mishra²

2018

Publ Inst Math (Belgr)

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“…Some of them give sharper estimates than the results proved by Quade [6], Mohapatra and Russell [7], and himself earlier [8]. These results of Chandra [5] are improved in different directions by different investigators such as Leindler [9] who dropped the monotonicity on generating sequence { } and Mittal et al [10,11] who used more general matrix while very recently Deger et al [12] used more general -method in view of Armitage and Maddox [1].…”

Section: Introductionmentioning

confidence: 82%

Approximation of Signals (Functions) by Trigonometric Polynomials inLp-Norm

Mittal

Singh

2014

International Journal of Mathematics and Mathematical Sciences

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Mittal and Rhoades (1999, 2000) and Mittal et al. (2011) have initiated a study of error estimatesEn(f)through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrixTdoes not have monotone rows. In this paper, the first author continues the work in the direction forTto be aNp-matrix. We extend two theorems on summability matrixNpof Deger et al. (2012) where they have extended two theorems of Chandra (2002) usingCλ-method obtained by deleting a set of rows from Cesàro matrixC1. Our theorems also generalize two theorems of Leindler (2005) toNp-matrix which in turn generalize the result of Chandra (2002) and Quade (1937).

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“…The Fourier approximation of signals (functions) that originated from the second theorem of Weierstrass has become an exciting interdisciplinary field of research for the last 130 years. These approximations have assumed important new dimensions due to their wide applications in signal analysis [31], in general and in digital signal processing [32] in particular, in view of the classical Shannon sampling theorem [7]. …”

Section: Main Results and Discussionmentioning

confidence: 99%