Sharp integral inequalities based on general Euler two-point formulae

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.

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Generalisation of a corrected Simpson's formula

The ANZIAM Journal ◽

10.1017/s1446181100009895 ◽

2006 ◽

Vol 47 (3) ◽

pp. 367-385 ◽

Cited By ~ 4

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.

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On Euler midpoint formulae

The ANZIAM Journal ◽

10.1017/s144618110000835x ◽

2005 ◽

Vol 46 (3) ◽

pp. 417-438 ◽

Cited By ~ 8

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.

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On the Error of Extended Gaussian Quadrature Formulae for Functions of Bounded Variation

Approximation and Computation: A Festschrift in Honor of Walter Gautschi ◽

10.1007/978-1-4684-7415-2_11 ◽

1994 ◽

pp. 169-178 ◽

Cited By ~ 1

Author(s):

Sven Ehrich

Keyword(s):

Bounded Variation ◽

Gaussian Quadrature ◽

Functions Of Bounded Variation ◽

Quadrature Formulae

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

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100023926 ◽

1948 ◽

Vol 44 (1) ◽

pp. 8-12 ◽

Cited By ~ 1

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.

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On generalization of weighted Ostrowski type inequalities for functions of bounded variation

Asian-European Journal of Mathematics ◽

10.1142/s1793557118500493 ◽

2018 ◽

Vol 11 (04) ◽

pp. 1850049 ◽

Cited By ~ 2

Author(s):

Huseyin Budak ◽

Mehmet Zeki Sarikaya

Keyword(s):

Bounded Variation ◽

Integral Inequalities ◽

Functions Of Bounded Variation ◽

Special Cases ◽

Type Integral

In this paper, some generalization of weighted Ostrowski type integral inequalities for mappings of bounded variation are obtained and some interesting inequalities as special cases are given.

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Approximation Properties of a Certain Modification of Durrmeyer Operators

10.21203/rs.3.rs-522598/v1 ◽

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.

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ON GENERALIZED FRACTIONAL INTEGRAL INEQUALITIES FOR FUNCTIONS OF BOUNDED VARIATION WITH TWO VARIABLES

Математички билтен/BULLETIN MATHÉMATIQUE DE LA SOCIÉTÉ DES MATHÉMATICIENS DE LA RÉPUBLIQUE MACÉDOINE ◽

10.37560/matbil21451049k ◽

2021 ◽

Vol 45 (1) ◽

pp. 49-69

Author(s):

ARTION KASHURI ◽

HŰSEYIN BUDAK ◽

ROZANA LIKO ◽

MUHAMMAD AAMIR ALI ◽

KUBILAY ÖZÇELIK

Keyword(s):

Bounded Variation ◽

Fractional Integral ◽

Integral Inequalities ◽

Functions Of Bounded Variation ◽

Generalized Fractional Integral

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Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and applications

Filomat ◽

10.2298/fil1716305b ◽

2017 ◽

Vol 31 (16) ◽

pp. 5305-5314 ◽

Cited By ~ 3

Author(s):

Hüseyin Budaka ◽

Mehmet Sarikaya ◽

Ather Qayyum

Keyword(s):

Bounded Variation ◽

Integral Inequalities ◽

Quadrature Formulae ◽

Special Cases ◽

Type Integral

The main aim of this paper is to obtain a improved and generalized version of companion of Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation. Some previous results are also recaptured as special cases. New quadrature formulae are also provided.

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