A generalization of the peano kernel and its applications

Recently, in [Electron. Trans. Numer. Anal. 41 (2014) 420–442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational cubic splines and investigated their basic shape preserving properties. The main goal of the current paper is to embark on univariate constrained fractal interpolation that is more general than what was considered so far. To this end, we propose some strategies for selecting the parameters of the rational fractal spline so that the interpolating curves lie strictly above or below a prescribed linear or a quadratic spline function. Approximation property of the proposed rational cubic fractal spine is broached by using the Peano kernel theorem as an interlude. The paper also provides an illustration of background theory, veined by examples.

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Design of Fractional Delay Filter, Differintegrator, Fractional Hilbert Transformer, and Differentiator in Time Domain With Peano Kernel

IEEE Transactions on Circuits and Systems I Regular Papers ◽

10.1109/tcsi.2009.2027806 ◽

2010 ◽

Vol 57 (2) ◽

pp. 391-404 ◽

Cited By ~ 14

Author(s):

Soo-Chang Pei ◽

Peng-Hua Wang ◽

Chia-Huei Lin

Keyword(s):

Time Domain ◽

Hilbert Transformer ◽

Fractional Delay ◽

Fractional Delay Filter ◽

Peano Kernel

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Peano kernel associated with the polyharmonic mean value property in the annulus

Numerical Functional Analysis and Optimization ◽

10.1080/01630560008816980 ◽

2000 ◽

Vol 21 (5-6) ◽

pp. 683-692 ◽

Cited By ~ 1

Author(s):

Werner Haußmann ◽

Ognyan Kounchev

Keyword(s):

Mean Value ◽

Mean Value Property ◽

Peano Kernel

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Peano kernel behaviour and error bounds for symmetric quadrature formulas

Computers & Mathematics with Applications ◽

10.1016/0898-1221(95)00004-i ◽

1995 ◽

Vol 29 (6) ◽

pp. 27-34 ◽

Cited By ~ 2

Author(s):

P. Favati ◽

G. Lotti ◽

F. Romani

Keyword(s):

Error Bounds ◽

Quadrature Formulas ◽

Peano Kernel

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A generalized Peano Kernel Theorem for distributions of exponential decay

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2015.07.072 ◽

2016 ◽

Vol 433 (1) ◽

pp. 622-641

Author(s):

Jerome Blair ◽

Aaron Luttman ◽

Eric Machorro

Keyword(s):

Exponential Decay ◽

Peano Kernel ◽

Kernel Theorem

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Ostrowski type inequalities and some selected quadrature formulae

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm200609054m ◽

2020 ◽

pp. 54-54

Author(s):

Gradimir Milovanovic

Keyword(s):

Numerical Integration ◽

Error Term ◽

Quadrature Formulas ◽

Quadrature Formulae ◽

Survey Paper ◽

Ostrowski’S Inequality ◽

Basic Facts ◽

Peano Kernel

Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D. S. Mitrinovic, who left us 25 years ago. His significant inuence to the development of the theory of inequalities is briefly given in the first section of this paper. Beside some basic facts on quadrature formulas and an approach for estimating the error term using Ostrowski type inequalities and Peano kernel techniques, we give several examples of selected quadrature formulas and the corresponding inequalities, including the basic Ostrowski's inequality (1938), inequality of Milovanovic and Pecaric (1976) and its modifications, inequality of Dragomir, Cerone and Roumeliotis (2000), symmetric inequality of Guessab and Schmeisser (2002) and asymmetric in-equality of Franjic (2009), as well as four point symmetric inequalites by Alomari (2012) and a variant with double internal nodes given by Liu and Park (2017).

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