Multivariate fractional Ostrowski type inequalities
Abstract
Optimal upper bounds are given for the deviation of a value of a multivariate function of a fractional space from its average, over convex and compact subsets of RN, N ≥ 2. In particular we work over rectangles, balls and spherical shells. These bounds involve the supremum and L∞ norms of related multivariate fractional derivatives of the function involved. The inequalities produced are sharp, namely they are attained. This work has been motivated by the works of Ostrowski [A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funcktion von ihrem Integralmittelwert, Commentarii Mathematici Helvetici 10 (1938) 226-227], 1938, and of the author [G.A. Anastassiou, Fractional Ostrowski type inequalities, Communications in Applied Analysis 7 (2) (2003) 203-208], 2003. © 2007 Elsevier Ltd. All rights reserved.
Publication Title
Computers and Mathematics with Applications
Recommended Citation
Anastassiou, G. (2007). Multivariate fractional Ostrowski type inequalities. Computers and Mathematics with Applications, 54 (3), 434-447. https://doi.org/10.1016/j.camwa.2007.01.024
