Abstract
We establish some Ostrowski type inequalities involving higher-order partial derivatives for two-dimensional integrals on Lebesgue spaces (L_{∞}, L_{p} and L₁). Some applications in Numerical Analysis in connection with cubature formula are given. Finally, with the help of obtained inequality, we establish applications for the kth moment of random variables.
Highlights
Let f : [a, b]→ R be a differentiable mapping on (a, b) whose derivative f : (a, b)→ R is bounded on (a, b), i.e., f ∞ = sup |f (t)| < ∞
In [7], [8] and [9], some Ostrowski type inequalities for double integrals and applications in numerical analysis in connection with cubature formula are given by researchers
We deal with applications of the integral inequalities developed in the previous section, to obtain estimates of cubature formula, which it turns out to have a markedly smaller error than that which may be obtained by the classical results
Summary
In [7], [8] and [9], some Ostrowski type inequalities for double integrals and applications in numerical analysis in connection with cubature formula are given by researchers. Some researchers established some Ostrowski type inequalities for n-times differentiable mappings in [1], [6] and [11]. In [10], weighted integral inequalities for one variable mappings which are n−times differentiable are obtained by Erden and Sarıkaya. The researchers established some Ostrowski type inequalities involving higher-order partial derivatives for double integrals in [4], [12] and [21]. Some applications of the Ostrowski type inequality developed in this work for cubature formula and the kth moment of random variables are given
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
