References
- [1] M.W. Alomari, Two-point Ostrowski’s inequality, Results in Mathematics, 72 (3) (2017), 1499–1523.10.1007/s00025-017-0720-6
- [2] M.W. Alomari, On Beesack–Wirtinger inequality, Results in Mathematics, 72 (3) (2017), 1213–1225.10.1007/s00025-016-0644-6
- [3] M.W. Alomari and S.S. Dragomir, Mercer-Trapezoid rule for Riemann–Stieltjes integral with applications, Journal of Advances in Mathematics, 2 (2) (2013), 67–85.
- [4] M.W. Alomari, A companion of Ostrowski’s inequality for the Riemann-Stieltjes integral ∫abf(t) du(t)$\int_a^b {f(t)} \,du(t)$, where f is of bounded variation and u is of r-H-Hölder type and applications, Appl. Math. Comput., 219 (2013), 4792–4799.10.1016/j.amc.2012.10.105
- [5] M.W. Alomari, New sharp inequalities of Ostrowski and generalized trapezoid type for the Riemann–Stieltjes integrals and applications, Ukrainian Mathematical Journal, 65 (7) 2013, 895–916.10.1007/s11253-013-0837-z
- [6] M.W. Alomari, Approximating the Riemann-Stieltjes integral by a three-point quadrature rule and applications, Konuralp J. Math., 2 (2) (2014), 2234.
- [7] M.W. Alomari, Two point Gauss-Legendre quadrature rule for Riemann-Stieltjes integrals, Preprint (2014). Avaliable at https://arxiv.org/pdf/1402.4982.pdf
- [8] M.W. Alomari, A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications, Ann. Univ. Paedagog. Crac. Stud. Math., 15 (2016), 69–78.
- [9] M.W. Alomari and S.S. Dragomir, A three-point quadrature rule for the Riemann-Stieltjes integral, Southeast Asian Bulletin Journal of Mathematics, in press
- [10] N.S. Barnett, S.S. Dragomir and I. Gomma, A companion for the Ostrowski and the generalised trapezoid inequalities, Mathematical and Computer Modelling, 50 (2009), 179–187.10.1016/j.mcm.2009.04.005
- [11] N.S. Barnett, W.-S. Cheung, S.S. Dragomir, A. Sofo, Ostrowski and trapezoid type inequalities for the Stieltjes integral with Lipschitzian integrands or integrators, Computer & Mathematics with Applications, 57 (2009), 195–201.10.1016/j.camwa.2007.07.021
- [12] P. Cerone, S.S. Dragomir, New bounds for the three-point rule involving the Riemann-Stieltjes integrals, in: C. Gulati, et al. (Eds.), Advances in Statistics Combinatorics and Related Areas, World Science Publishing, 2002, pp. 53–62.10.1142/9789812776372_0006
- [13] P. Cerone, S.S. Dragomir, Approximating the Riemann–Stieltjes integral via some moments of the integrand, Mathematical and Computer Modelling, 49 (2009), 242–248.10.1016/j.mcm.2008.02.011
- [14] S.S. Dragomir, On the Ostrowski inequality for Riemann–Stieltjes integral ∫abf(t) du(t)$$\int_a^b {f(t)} \,du(t) where f is of Hölder type and u is of bounded variation and applications, J. KSIAM, 5 (2001), 35–45.
- [15] S.S. Dragomir, On the Ostrowski’s inequality for Riemann-Stieltes integral and applications, Korean J. Comput. & Appl. Math., 7 (2000), 611–627.10.1007/BF03012272
- [16] S.S. Dragomir, C. Buşe, M.V. Boldea, L. Braescu, A generalisation of the trapezoid rule for the Riemann-Stieltjes integral and applications, Nonlinear Anal. Forum 6 (2) (2001) 33–351.
- [17] S.S. Dragomir, Some inequalities of midpoint and trapezoid type for the Riemann-Stieltjes integral, Nonlinear Anal. 47 (4) (2001) 2333–2340.10.1016/S0362-546X(01)00357-1
- [18] S.S. Dragomir, Approximating the Riemann-Stieltjes integral in terms of generalised trapezoidal rules, Nonlinear Anal. TMA 71 (2009) e62–e72.10.1016/j.na.2008.10.004
- [19] S.S. Dragomir, Approximating the Riemann-Stieltjes integral by a trapezoidal quadrature rule with applications, Mathematical and Computer Modelling 54 (2011) 243–260.10.1016/j.mcm.2011.02.006
- [20] W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Stat. Comput., 3 (1982), 289–317.10.1137/0903018
- [21] A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Th., 115 (2002), 260–288.10.1006/jath.2001.3658
- [22] P.R. Mercer, Hadamard’s inequality and trapezoid rules for the RiemannStieltjes integral, J. Math. Anal. Appl. 344 (2008) 921–926.10.1016/j.jmaa.2008.03.026
- [23] M. Munteanu, Quadrature formulas for the generalized Riemann-Stieltjes integral, Bull. Braz. Math. Soc. (N.S.) 38 (1) (2007) 39-50.10.1007/s00574-007-0034-5
- [24] M. Tortorella, Closed Newton-Cotes quadrature rules for Stieltjes integrals and numerical convolution of life distributions, SIAM J. Sci. Stat. Comput. 11 (1990) 732–748.10.1137/0911043