Stieltjes integrals
On Ostrowski Type Inequalities for Stieltjes Integrals with Absolutely Continuous Integrands and Integrators of Bounded Variation
... for Stieltjes integrals R a b f (t) du (t) where the function f, the integrand, is assumed to be absolutely continuous while the integrator u, is of bounded vari- ...
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Majorisation Inequalities for Stieltjes Integrals
... Theorem 5. Let F : I ⊆ R → R be a convex function on the interval I and x, y, p : [a, b] → I with p (x) ≥ 0 for x ∈ [a, b] . If ϕ ∈ ∂F, u : [a, b] → I is a monotonic nondecreasing function on [a, b] and such that the ...
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Oscillation of impulsive functional differential equations with oscillatory potentials and Riemann Stieltjes integrals
... This paper addresses the oscillation problem of a class of impulsive differential equations with delays and Riemann-Stieltjes integrals that cover many equations in the literature. In the case of oscillatory ...
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On Henstock Stieltjes Integrals of Interval Valued Functions and Fuzzy Number Valued Functions
... As it is well known, the Henstock (H) integral for a real function was first defined by Henstock [1] in 1963. The Henstock (H) integral is a lot powerful and easier than the Lebesgue, Wiener and Richard Phillips Feynman ...
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A new inequality for the Riemann Stieltjes integrals driven by irregular signals in Banach spaces
... To obtain the convergence of Riemann-Stieltjes sums, we will use a partial solution of a variational problem similar to that considered in [1]. In [1] the following problem was considered: given real a < b, c ...
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Lebesgues Stieltjes Integrals of Fuzzy Stochastic Processes with Respect to Finite Variation Processes
... In [21], the author studied the Lebesgue-Stieltjes integral of real stochastic processes with respect to fuzzy va- lued stochastic processes. In some references such as [5] [6], the integrals of fuzzy ...
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On McShane-Stieltjes Integrals of Interval-valued Functions and Fuzzy-number-valued Functions on Time Scales
... Definition 1. [10] Let α : [a, b] → R be an increasing function. A real-valued function f : [a, b] → R is said to be McShane-Stieltjes (M S) integrable to B with respect to α on [a, b] if for every ε > 0, there ...
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Inequalities for Stieltjes Integrals with Convex Integrators and Applications
... Inequalities for a Gr¨ uss type functional in terms of Stieltjes inte- grals with convex integrators are given.. Applications to the ˇ Cebyˇ sev functional are also provided1[r] ...
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Approximating the Stieltjes Integral for (φ, ф)-Lipschitzian Integrators and Applications
... DRAGOMIR, On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation, Preprint RGMIA Res.. CERONE and S.S.[r] ...
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GENERAL THREE POINTS INEQUALITIES FOR WEIGHTED RIEMANN-STIELTJES INTEGRAL
... [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 ...
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Alternatives in calculating double integrals
... Key Words: Double Integral, Center Of Mass, Area, Substitution, Region, Moment, Ellipse, Major Axis, Minor Axis, Interior, Boundary.. This is an open access article distributed under the[r] ...
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Stieltjes transforms on new generalized functions
... 3. Integration on new tempered generalized functions. The Stieltjes transform will require an integration process in a somewhat similar manner as does the Fourier transform. Since distributional integration eluded ...
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Riemann Stieltjes Operators between Vector Valued Weighted Bloch Spaces
... compact between B α X and B β X except for the trivial case that g is a constant function. In this paper, we will study some small property of Riemann-Stieltjes operators between X-valued Bloch spaces. The main ...
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Solving Real Integrals Using Complex Integrals
... real integrals of trigonometric ...real integrals can be obtained using complex ...definite integrals and their solutions for verifying our ...
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Operational calculus on fourier stieltjes transform
... The operational calculus of Integral transform essentially involves the replacement of the function under the study by other functions called transform, which are obtained from the original functions by certain rules. ...
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Application of Integrals
... In the previous chapter, we have studied to find the area bounded by the curve y = f (x), the ordinates x = a, x = b and x-axis, while calculating definite integral as the limit of a sum. Here, in this chapter, we shall ...
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On geometric fractional calculus
... Abstract. In this paper, we set the main concepts for geometric (multiplicative) fractional calculus. We define Caputo, Riemann and Letnikov multiplicative fractional derivatives and multiplicative fractional ...
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Iterated Stieltjes transform of generalized functions
... Our main objective in this paper is to extend the transform 1.4’ to generalized functions, and to prove the inversion formula 1.5 in the distributional sense.. The distributional extensi[r] ...
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Fourier-Stieltjes Transform of Some Functions
... Where, ( ) is output, ( , ) is Kernel, ( ) is input. In this, the Kernel and Interval remain the same for a transform irrespective of the input function. The input and output functions changes depending on the problems ...
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02 Trigonometric Integrals - Handout.pdf
... Trig Integrals Trig Integrals Trig Integrals Exercises tan sec or cot csc sin mx cos nx dx , sin mxsin nx dx or cos mxcos nx dx Trigonometric Integrals. Integrals of the form R[r] ...
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