General Multivariate Iyengar Type Inequalities

Year 2019, , 64 - 80, 01.06.2019

George Anastassıou

https://doi.org/10.33205/cma.543560

Cited By: 6

Abstract

Here we give a variety of general multivariate Iyengar type inequalities for not necessarily radial functions defined on the shell and ball. Our approach is based on the polar coordinates in $\mathbb{R}^{N}$, $N\geq 2$, and the related multivariate polar integration formula. Via this method we transfer well-known univariate Iyengar type inequalities and univariate author's related results into general multivariate Iyengar inequalities.

Keywords

Iyengar inequality, Polar coordinates, Shell, Not necessarily radial function, Ball

References

• [1] R. P. Agarwal, S. S. Dragomir: An application of Hayashi’s inequality for differentiable functions, Computers Math. Applic., 6 (1996), 95-99.
• [2] G. A. Anastassiou: Fractional Differentiation Inequalities, Research Monograph, Springer, New York, 2009.
• [3] G. A. Anastassiou: General Iyengar type inequalities, submitted, 2018.
• [4] Xiao-Liang Cheng: The Iyengar-type inequality, Applied Math. Letters 14 (2001), 975-978.
• [5] K. S. K. Iyengar: Note on an inequality, Math. Student 6, (1938), 75-76.
• [6] Zheng Liu: Note on Iyengar’s inequality, Univ. Beograd Publ. Elektrotechn. Fak., Ser. Mat. 16 (2005), 29-35.
• [7] F. Qi: Further generalizations of inequalities for an integral, Univ. Beograd Publ. Elektrotechn. Fak., Ser. Mat. 8 (1997), 79-83.
• [8] W. Rudin: Real and Complex Analysis, International Student edition, Mc Graw Hill, London, New York, 1970.
• [9] D. Stroock: A Concise Introduction to the Theory of Integration, Third Edition, Birkhaüser, Boston, Basel, Berlin, 1999.