Dragomir, Sever S. Inequalities for Stieltjes integrals with convex integrators and applications. (English) Zbl 1116.26004 Appl. Math. Lett. 20, No. 2, 123-130 (2007). The author considers the following functional: \[ D(f:u):= \int^b_a f(x)du(x)-(u(b)-u(a)) {1\over b-a} \int^b_a f(t)\,dt \]provided that the Stieltjes integral and Riemann integral exist. The main aim of this work is to establish sharp inequalities for the functional \(D(.,.)\) on the assumption that the integrator \(u\) in the Stieltjes integral \(\int^b_a f(x) du(x)\) is convex on \([a,b]\). Applications for the Chebyshev functional of two Lebesgue integrable functions are also given. Reviewer: Octavian Lipovan (Timişoara) Cited in 17 Documents MSC: 26A42 Integrals of Riemann, Stieltjes and Lebesgue type 26D15 Inequalities for sums, series and integrals Keywords:Grüss inequality; Chebyshev inequality; convex functions PDF BibTeX XML Cite \textit{S. S. Dragomir}, Appl. Math. Lett. 20, No. 2, 123--130 (2007; Zbl 1116.26004) Full Text: DOI OpenURL References: [1] Dragomir, S.S., Inequalities of grüss type for the Stieltjes integral and applications, Kragujevac J. math, 26, 89-112, (2004) · Zbl 1274.26035 [2] Dragomir, S.S.; Fedotov, I., A grüss type inequality for mappings of bounded variation and applications to numerical analysis, Nonlinear funct. anal. appl., 6, 3, 425-433, (2001) · Zbl 0995.26012 [3] Dragomir, S.S.; Fedotov, I., An inequality of grüss type for riemann – stieltjes integral and applications for special means, Tamkang J. math., 29, 4, 287-292, (1998) · Zbl 0924.26013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.