A Companion of Ostrowski inequality for the Stieltjes integral of monotonic functions

Mohammad Alomari

doi:10.55059/ijm.2022.1.2/20

Authors

Mohammad Alomari Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid https://orcid.org/0000-0002-6696-9119

DOI:

https://doi.org/10.55059/ijm.2022.1.2/20

Keywords:

Ostrowski’s inequality, bounded variation, Riemann-Stieltjes integral

Abstract

Some companions of Ostrowski’s integral inequality for the RiemannStieltjes integral \int_a^b{ f (t) du (t)}, where f is assumed to be of r-H-H¨older type on [a, b] and u is of monotonic non-decreasing on [a, b], are proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.

Author Biography

Mohammad Alomari, Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid

Prof. Alomari is a Full Professor of Mathematics (Mathematical Analysis) at Irbid National University-Jordan. He was awarded his Ph.D. from Universiti Kebangsaan Malaysia in 2011. His main research area includes; Mathematical inequalities, Approximation theory, Hilbert space, and classical theory of real functions. Since 2008 Prof. Alomari published more than 80 articles in his area of research and he had done two book drafts both of them within his main research interests in Mathematical Inequalities. Prof. Alomari has other research interests such as the theory of complex variables and ordinary differential equations, where he had finished many drafts in these two areas.

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