Some applications of quadrature rules for mappings on \(L_p[u,v]\) space via Ostrowski-type inequality

Authors

  • Nazia Irshad Department of Mathematics, University of Karachi http://orcid.org/0000-0001-6711-3358
  • Asif R. Khan Department of Mathematics, University of Karachi, Pakistan

DOI:

https://doi.org/10.33993/jnaat462-1107

Keywords:

Ostrowski inequality, Lp space, bounded variation, numerical integration, sharp bounds
Abstract views: 340

Abstract

Some Ostrowski-type inequalities are stated for \(L_p[u,v]\) spaces and for mappings of bounded variations. Applications are also given for obtaining error bounds of some composite quadrature formulae.

Downloads

Download data is not yet available.

References

M. W. Alomari, A Companion of Dragomir’s Generalization of the Ostrowski inequality and Applications to Numerical integration, Ukrainian Mathematical Journal, 64 (4), (2012), pp. 491-509, DOI: https://doi.org/10.1007/s11253-012-0661-x

P. L. Chebyshev, Sur les expressions approximative des integrals par les auters prises entre les memes limites, Proc. Math. Soc. Charkov, 2 (1882), pp. 93-98.

S. S. Dragomir and S.Wang, An inequality of Ostrowski-Gr ̈uss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl., 33 (1997), pp. 15-20, DOI: https://doi.org/10.1016/S0898-1221(97)00084-9

S. S. Dragomir, A Companion of Ostrowski’s Inequality for functions of Bounded Variation and Applications, Int. J. Nonlinear Anal. Appl., 5 (2014), pp. 89-97.

G. Gruss, Uber das Maximum des absoluten Betragesvon 1(b−a)∫baf(x)g(x)dx−1(b−a)2×∫bf(x)dx∫bag(x)dx , Math. Z., 39 (1935), pp. 215-226. DOI: https://doi.org/10.1007/BF01201355

Asif R. Khan, Josip Pecaric and M. Praljak, Weighted Montgomery inequalities for higher order differentiable functions of two variables, Rev. Anal. Numer. Theor. Approx., 42 (1) (2013), pp. 49-71.

Mohammas Masjed-Jamei and Severs. Dragomir Generalization of Ostrowski-Gruss Inequality, World Scientific, 12 (2) (2014), pp. 117-130, DOI: https://doi.org/10.1142/S0219530513500309

G. V. Milovanovic, On some integral inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., No. 498–541 (1975), pp. 119-124.

G.V. Milovanovic, J. E. Pecaric, On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., No. 544-576 (1976), pp. 155-158.

A. M. Ostrowski, Uber die absolutabweichung einer differentiebaren funktion von ihren integralmittelwert, Comment. Math. Helv., 10 (1938), pp. 226-227, DOI: https://doi.org/10.1007/BF01214290

Richard L. Wheeden and Antoni Zygmund, Measure and Integral, Marcel Dekker. Inc, New York, 1977. DOI: https://doi.org/10.1201/b15702

Downloads

Published

2017-11-08

How to Cite

Irshad, N., & Khan, A. R. (2017). Some applications of quadrature rules for mappings on \(L_p[u,v]\) space via Ostrowski-type inequality. J. Numer. Anal. Approx. Theory, 46(2), 141–149. https://doi.org/10.33993/jnaat462-1107

Issue

Section

Articles