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





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


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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S.S. Dragomir and Th.M. Rassias (Ed.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publishers, Dordrecht, 2002.


S.S. Dragomir, On the Ostrowski inequality for Riemann-Stieltjes integral ∫_a^bf(t)du(t) where f is of H ̈older type and u is of bounded variation and applications, J. KSIAM, 5 (2001), 35-45.

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S.S. Dragomir, Some inequalities of midpoint and trapezoid type for the Riemann-Stieltjes integral, Nonlinear Anal. 47 (4) (2001) 2333-2340.


S.S. Dragomir, Approximating the Riemann-Stieltjes integral by a trapezoidal quadrature rule with applications, Mathematical and Computer Modelling 54 (2011) 243-260.


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How to Cite

Alomari, M. (2022). A Companion of Ostrowski inequality for the Stieltjes integral of monotonic functions. Innovative Journal of Mathematics (IJM), 1(2), 18–29. https://doi.org/10.55059/ijm.2022.1.2/20