scholarly journals Generalisation of a corrected Simpson's formula

2006 ◽  
Vol 47 (3) ◽  
pp. 367-385 ◽  
Author(s):  
J. Pečarić ◽  
I. Franjić
Keyword(s):  
Error Estimates ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Lipschitzian Functions ◽  
Integrable Functions

AbstractThe results obtained by A. J. Roberts and N. Ujević in a recent paper are generalised. A number of inequalities for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or R-integrable functions are derived. Also, some error estimates for the derived formulae are obtained.

scholarly journals Sharp integral inequalities based on general Euler two-point formulae

2005 ◽  
Vol 46 (4) ◽  
pp. 555-574 ◽  
Author(s):  
J. Pečarić ◽  
I. Perić ◽  
A. Vukelić
Keyword(s):  
Bounded Variation ◽  
Integral Inequalities ◽  
Functions Of Bounded Variation ◽  
Quadrature Formulae ◽  
Lipschitzian Functions ◽  
Integrable Functions

AbstractWe consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or R-integrable functions, are proved.

A note on the representation of functions by absolutely convergent fourier integrals

1948 ◽  
Vol 44 (1) ◽  
pp. 8-12 ◽  
Author(s):  
H. R. Pitt
Keyword(s):  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Integrable Functions ◽  
Image Position ◽  
Class Of Functions ◽  
Fourier Integrals

1. We write L for the class of integrable functions in (− ∞, ∞), V for the class of functions of bounded variation, and define A, A to be the classes of functions F(x) which may be expressed in the formsrespectively.

ON A GENERALISED TRAPEZOIDAL RULE FOR FUNCTIONS OF BOUNDED VARIATION

2009 ◽  
Vol 02 (02) ◽  
pp. 191-200
Author(s):  
P. Cerone ◽  
S. S. Dragomir ◽  
A. McAndrew
Keyword(s):  
Error Estimates ◽  
Bounded Variation ◽  
Trapezoidal Rule ◽  
Functions Of Bounded Variation

A generalised trapezoidal rule is considered. Error estimates for functions of bounded variation are given. Applications for some particular cases of interest are provided as well.

scholarly journals Approximation Properties of a Certain Modification of  Durrmeyer Operators

2021 ◽  
Author(s):  
Asha Ram Gairola ◽  
Karunesh Kumar Singh ◽  
Hassan Khosravian Arab ◽  
Vishnu Narayan Mishra
Keyword(s):  
Error Estimate ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Approximation Properties ◽  
Numerical Examples ◽  
Durrmeyer Operators ◽  
Integrable Functions ◽  
Durrmeyer Operator ◽  
Bézier Variant

Abstract We study approximation properties of a new operator DM,1 n (f, x) introduced by Acu et al. in [Results Math 74:90, (2019)] for Lebesgue integrable functions in [0,1]. An error estimate by the Bezier variant of the operators DM,1 n (f, x)is also obtained for the functions of bounded variation. By relevant numerical examples, the orders of approximation by the operator DM,1 n (f, x) and the modified-Bernstein-Durrmeyer operator are also compared.

scholarly journals On Euler midpoint formulae

2005 ◽  
Vol 46 (3) ◽  
pp. 417-438 ◽  
Author(s):  
LJ. Dedić ◽  
M. Matić ◽  
J. Pečarić
Keyword(s):  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Quadrature Formulae ◽  
Lipschitzian Functions

AbstractModified versions of the Euler midpoint formula are given for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or functions in Lp-spaces. The results are applied to quadrature formulae.

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

scholarly journals Some Bounds for the Complex Čebyšev Functional of Functions of Bounded Variation

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 990
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Functional Applications ◽  
Čebyšev Functional

In this paper, we provide several bounds for the modulus of the complex Čebyšev functional. Applications to the trapezoid and mid-point inequalities, that are symmetric inequalities, are also provided.

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