Paper's Title:

Three Points Inequalities For Riemann-Stieltjes Integral of Lipschitzian or Bounded Variation Integrands and Integrators of R-H Holder Type With Applications

Author(s):

N. A. Alsubaie^1,2, Sever S. Dragomir^1,3, G. Sorrentino⁴

¹ISILC,
Victoria University,
PO Box 14428, Melbourne City, MC 8001,VIC
Australia.
E-mail: nawal.alsubaie@live.vu.edu.au sever.dragomir@vu.edu.au sever.dragomir@ajmaa.org

²Mathematics Department,
Khurmah University College, Taif University,
KSA.
e-mail: nawal.s@tu.edu.sa

³DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science, and Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.

 
⁴Mathematics, First Year College, Victoria University, PO Box 14428,
Melbourne City, MC 8001, VIC
Australia.
E-mail: Gabriele.Sorrentino@vu.edu.au
 

Abstract:

In this paper we obtained some new simple error bounds in approximating the Riemann-Stieltjes integral ∫_a^bf (t) du (t) by the use of three points rule

where λ, υ ∈ [ 0,1] , x∈ [ a,b ] and assuming that the function f is L-Lipschitzian or of bounded variation and u is r-H-Hölder type on [a,b] . The important case of weighted integrals is considered, compounding quadrature rules are provided and applications for approximation of Fourier transforms on finite intervals are also given.

Paper's Title:

Some Ostrowski Type Inequalities for Two Cos-Integral Transforms of Absolutely Continuous Functions

Author(s):

S. S. Dragomir and G. Sorrentino

Mathematics, College Sport, Health and Engineering,
Victoria University, PO Box 14428,
Melbourne City, MC 8001,
Australia.

DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.
E-mail: sever.dragomir@vu.edu.au
URL: http://rgmia.org/dragomir

Mathematics, First Year College,
Victoria University, PO Box 14428,
Melbourne City, MC 8001,
Australia.
 

Abstract:

For a Lebesgue integrable function f:[a,b] ⊂[0,π]→C we consider the cos-integral transforms


and

We provide in this paper some upper bounds for the quantities

and

for
x ∈ [ a,b], in terms of the p-norms of the derivative f ' for absolutely continuous functions f:[a,b] ⊂[0,π]→C. Applications for approximating Steklov cos-average functions and Steklov split cos-average functions are also provided.

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