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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