[PDF] Top 20 Approximating the Riemann-Stieltjes integral via a Chebyshev type functional

... uss type for the Riemann-Stieltjes integral and applications for special means, Tamkang ...uss type inequality for mappings of bounded vari- ation and applications for numerical ... See full document

... in approximating the Riemann-Stieltjes integral a b f (t) du(t) with the generalised trapezoid formula f (b)[u(b) – b–a 1 a b u(s) ds] + f(a)[ b–a 1 a b u(s) ds – u(a)] are given for various ... See full document

... the Riemann-Stieltjes integral, in Advances in Statistics, Combinatorics and Related Areas, Chandra Gulati, Yan-Xia Lin, Satya Mishra and John Rayner ... See full document

... older type, which pro- vides a refinement for ...older type were considered by Cheung and Dragomir in [5], while the case where one function was of H¨ older type and the other was Lipschitzian were ... See full document

... FEDOTOV, An inequality of Gr¨ uss type for the Riemann-Stieltjes integral and applications for special means, Tamkang J. FEDOTOV, A Gr¨ uss type inequality for mappings of bounded[r] ... See full document

... of Riemann-Stieltjes integral a b f (t)du(t), where f is called the integrand, u is called the integrator, plays an important role in mathematics, for instance in the definition of complex ... See full document

... in approximating the Riemann-Stieltjes in- tegral with (l, L)-Lipschitzian integrators and applications for the ˇ Cebyˇ sev functional are ... See full document

... the Chebyshev in his famous paper [] and were subsequently rediscovered in various inequalities (for the celebrated functionals) by numerous authors, including Anastassiou [], Belarbi and Dahmani [], Dahmani et ... See full document

... for any continuous function f : [a, b] → C . Applications for the trapezoidal and midpoint inequalities are given. New inequali- ties for some ˇ Cebyˇ sev and (CBS)-type functionals are presented. Natural ... See full document

... the Riemann-Stieltjes integral, expressed in terms of the truncated variation functionals and derive from it the stronger version of the Loéve- Young ...of integral equations driven by ... See full document

... of Riemann-Stieltjes integral ∫ a b f (t) du(t), where f is called the integrand and u is called the integrator, plays an important role in Math- ematics, for instance in the definition of complex ... See full document

... [2] P. CERONE, S.S. DRAGOMIR and J. ROUMELIOTIS, Some Ostrowski type inequalities for n time di¤erentiable mappings and applications, Demonstratio Math., 32(2) (1999), 697-712. [3] P. CERONE, S.S. DRAGOMIR, J. ... See full document

... the Riemann-Stieltjes integral, where A is a function of bounded variation, and dA may be a signed ...and integral boundary problems as special ... See full document

... In general, the exact computation in the integral (1.2) is very complicated and from this point of view, the Poincar´e formula is only of theoretical interest [1]. The numerical integration can also be excessively ... See full document

... [r] ... See full document

... [5] M. T. Rashed, “Numerical Solution of Functional Differ- ential, Integral and Integro-Differential Equations,” Ap- plied Mathematics and Computation, Vol. 156, No. 2, 2004, pp. 485-492. ... See full document

... DRAGOMIR, A generalization of Gr¨ uss’ inequality in inner product spaces and appli- cations, J.. FEDOTOV, An inequality of Gr¨ uss’ type for Riemann-Stieltjes integral and applications [r] ... See full document

... [3] P. Cerone, W. S. Cheung and S. S. Dragomir, On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation, Comput. Math. Appl. 54 ... See full document

... Assume that u; f : [a; b] ! C . If the Riemann-Stieltjes integral R a b f (t) du (t) exists, we write for simplicity, like in [1, p. 142] that f 2 R C (u; [a; b]) ; or R C (u) when the interval is ... See full document

... Applica- tions for the generalised trapezoid formula and the Ostrowski inequality for functions of bounded variation are also provided1. Pollard [2] obtained by elementary arguments the [r] ... See full document