Weighted L p-Approximation of Derivatives by the Method of Gammaoperators

Lupas, Alexandru; Mache, Detlef H.; Müller, Manfred

doi:10.1007/bf03322258

Cited by 13 publications

(2 citation statements)

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“…The transform (1.1) reproduces distinct integral operators for different values of a, b, and r. The derived operators have been introduced and studied extensively by several researchers over the past few decades; for instance, see previous studies. [2][3][4][5][6] For b = 0, a = −1, and r = n + 1, we obtain one particular operator first introduced and studied by Lupaş and Müller 7 and also referred to as gamma operators. Let E be the space of all measurable complex-valued function f defined on the interval (0, ∞) and locally bounded in any subinterval [c, d], 0 < c < d < ∞.…”

Section: Introductionmentioning

confidence: 99%

Convergence estimates of certain gamma type operators

Mishra

Deo

2021

Math Methods in App Sciences

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The present paper deals with a modified form of gamma type operators that preserve the test functions es=ts,3.0235pts∈ℕ and estimation of their approximation properties. We begin by determining the convergence rate of the proposed operators in the sense of the usual modulus of continuity and Peetre's K‐functional. Further, the degree of approximation is also established for the function of bounded variation. We also illustrate via figures and tables that the proposed modification provides a better approximation for preserving the test function e3.

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Section: Introductionmentioning

confidence: 99%

Convergence estimates of certain gamma type operators

Mishra

Deo

2021

Math Methods in App Sciences

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“…In this paper, we introduce two families G and G* of gamma-type operators having the form (1.1) and given, respectively, by where [• ] stands for integral part. These operators differ from other gamma-type operators considered in the literature, such as the operator introduced by Lupas and Miiller [11] and investigated in subsequent papers (see, for instance, [10,14]) and the operator introduced by Khan [9] (see also [3]). We shall firstly mention some examples in which both operators arise in a natural way (we refer to [ 1,2] for more details).…”

Section: Introductionmentioning

confidence: 99%

Direct and converse inequalities for positive linear operators on the positive semi-axis

Adell

Sangüesa

1999

J Aust Math Soc A

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We consider positive linear operators of probabilistic type L,f acting on real functions / defined on the positive semi-axis. We deal with the problem of uniform convergence of L,f to / , both in the usual sup-norm and in a uniform L p type of norm. In both cases, we obtain direct and converse inequalities in terms of a suitable weighted first modulus of smoothness of/. These results are applied to the Baskakov operator and to a gamma operator connected with real Laplace transforms, Poisson mixtures and Weyl fractional derivatives of Laplace transforms.1991 Mathematics subject classification (Amer. Math. Soc): primary 44A10,41A35, 60J30.

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