scholarly journals A generalization of the peano kernel and its applications

2018 ◽  
Vol 67 (2) ◽  
pp. 229-241
Author(s):  
BUDAKÇI Gülter; ORUÇ
Keyword(s):  
Peano Kernel

scholarly journals TOWARDS A MORE GENERAL TYPE OF UNIVARIATE CONSTRAINED INTERPOLATION WITH FRACTAL SPLINES

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550040 ◽  
Author(s):  
A. K. B. CHAND ◽  
P. VISWANATHAN ◽  
K. M. REDDY
Keyword(s):  
Fractal Interpolation ◽  
Quadratic Spline ◽  
Constrained Interpolation ◽  
New Class ◽  
Background Theory ◽  
Fractal Interpolation Functions ◽  
Numer Anal ◽  
Shape Preserving Properties ◽  
Peano Kernel ◽  
Interpolation Functions

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.

scholarly journals A generalized Peano Kernel Theorem for distributions of exponential decay

2016 ◽  
Vol 433 (1) ◽  
pp. 622-641
Author(s):  
Jerome Blair ◽  
Aaron Luttman ◽  
Eric Machorro
Keyword(s):  
Exponential Decay ◽  
Peano Kernel ◽  
Kernel Theorem

scholarly journals Ostrowski type inequalities and some selected quadrature formulae

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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