Riemann–Stieltjes integral
Existence and uniqueness of solutions for systems of fractional differential equations with Riemann–Stieltjes integral boundary condition
... Let E be a real Banach space, P be a normal cone in E. In this section, we consider the existence and uniqueness of the solution as well as iterative approximation of the system of fractional differential equations (1.3) ...
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An Inequality of Grüss Type for Riemann-Stieltjes Integral and Applications for Special Means
... In this paper we derive a new inequality of Gr¨ uss’ type for Riemann- Stieltjes integral and apply it for special means (logarithmic mean, identric mean, etc...).. 1 Introduction.[r] ...
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Positive solutions of fractional differential equations involving the Riemann–Stieltjes integral boundary condition
... where 2 < α ≤ 3, 0 < β ≤ 1 are real numbers and 0 1 D β 0+ u(t) dA(t) denotes a Riemann– Stieltjes integral. By means of the monotone iterative technique and the inequalities asso- ciated with ...
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Existence and uniqueness of nontrivial solutions to a system of fractional differential equations with Riemann–Stieltjes integral conditions
... β is right continuous on [0, 1), left continuous at t = 1, and nondecreasing on [0, 1] with β(0) = 0, 0 1 u(τ ) dβ(τ ) denotes the Riemann–Stieltjes integral of u with respect to β . Here the ...
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Sharp error bounds in approximating the Riemann Stieltjes integral by a generalised trapezoid formula and applications
... 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 pairs (f, u) of ...
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A new theorem on the existence of the Riemann Stieltjes integral and an improved version of the Loéve Young inequality
... provided that the meshes(π) and (ρ) are sufficiently small. Since N may be arbitrarily large, we get the convergence of the approximating sums to an universal limit, which is the Riemann-Stieltjes ...
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ON SOME RIEMANN-STIELTJES INTEGRAL INEQUALITIES OF GENERALIZED TRAPEZOID TYPE WITH APPLICATIONS
... 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 ...
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Inequalities for the Riemann-Stieltjes integral of S-dominated integrators with applications. I
... [12] Dragomir S. S. Some inequalities of midpoint and trapezoid type for the Riemann–Stieltjes integral. Nonlinear Anal., 2001, vol. 47, pp. 2333–2340. [13] Dragomir S. S. Improvements of Ostrowski ...
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Generalizations of Opial’s Inequalities for Riemann-Stieltjes Integral with Applications
... Motivated by the above results, in this paper we establish some generalizations of Opial’s inequalities for Riemann-Stieltjes integral and for two functions2. Appli- cations related to t[r] ...
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Positive solutions of singular fractional order differential system with Riemann Stieltjes integral boundary condition
... Obviously, system () is more general than the problems discussed in some recent litera- ture. Firstly, the system depends on two parameters; secondly, the nonlinear terms f and g are allowed to have different nonlinear ...
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Positive solutions of Riemann Stieltjes integral boundary problems for the nonlinear coupling system involving fractional order differential
... investigated in [, , –]. To the best of our knowledge, there are only few papers deal- ing with the existence, multiplicity, and nonexistence of positive solutions of Riemann- Stieltjes ...
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Approximating the Riemann-Stieltjes Integral via Some Moments of the Integrand
... the Riemann-Stieltjes integral, in Advances in Statistics, Combinatorics and Related Areas, Chandra Gulati, Yan-Xia Lin, Satya Mishra and John Rayner ...
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Differences Between Means with Bounds from a Riemann-Stieltjes Integral
... Abstract. An identity for the difference between two integral means is ob- tained in terms of a Riemann-Stieltjes integral. This enables bounds to be procured when the integrand is of bounded ...
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Approximating the Riemann-Stieltjes Integral via a Čebyšev Type Functional
... 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] ...
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Sharp Error Bounds in Approximating the Riemann-Stieltjes Integral by a Generalised Trapezoid Formula and Applications
... [1] Barnett, N.S.; Cheung, W.-S.;Dragomir, S.S. and Sofo, A.;Ostrowski and trapezoid type inequalities for the Stieltjes integral with Lipschitzian integrands or integrators, Preprint, RGMIA Res. Rep. ...
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Approximating the Riemann Stieltjes integral of smooth integrands and of bounded variation integrators
... Theorem Assume that the function f : I → C is n-times differentiable on the interior I ˚ of the interval I (n ≥ ) and the nth derivative f (n) is of locally bounded variation on ˚ I. If a, b ∈ I with a ˚ < b, c ∈ ...
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A Sharp Bound of the Čebyšev Functional for the Riemann-Stieltjes Integral and Applications
... Applications for quadrature rules including the trapezoid and mid-point rule are given1. Cebyˇ ˇ sev functional, Riemann-Stieltjes integral, Trapezoid and mid- point rules, Quadrature ru[r] ...
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Approximating the Riemann-Stieltjes integral via a Chebyshev type functional
... [11] S. S. Dragomir and I. Fedotov, An inequality of Gr¨ uss type for the Riemann-Stieltjes integral and applications for special means, Tamkang J. Math., 29(4) (1998), 287–292. [12] S. S. Dragomir ...
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A Generalisation of the Trapezoidal Rule for the Riemann-Stieltjes Integral and Applications
... The following corollary which provides an upper bound for the approximation error in the trapezoid quadrature formula, for f of bounded variation, holds [4].. Corollary 2.[r] ...
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The Beesack-Darst-Pollard Inequalities and Approximation of the Riemann-Stieltjes Integral
... DRAGOMIR, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Mathematical Inequalities and Applications, 4(1) (2001), 59-66.. [6] S.S.[r] ...
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