Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2009, Article ID 432857, 14 pages doi:10.1155/2009/432857 Research Article An Extension of Stolarsky Means to the Multivariable Case Slavko Simic Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, Serbia Correspondence should be addressed to Slavko Simic, ssimic@turing.mi.sanu.ac.rs Received 10 July 2009; Accepted 23 September 2009 Recommended by Feng Qi We give an extension of well-known Stolarsky means to the multivariable case in a simple and applicable way. Some basic inequalities concerning this matter are also established with applications in Analysis and Probability Theory. Copyright q 2009 Slavko Simic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction There is a huge amount of papers investigating properties of the so-called Stolar- sky or extended two-parametric mean value, defined for positive values of x, y, as E r,s ( x, y ) : r ( x s - y s ) s ( x r - y r ) 1/s-r , rsr - s ( x - y ) / 0. 1.1 E means can be continuously extended on the domain ( r, s; x, y ) | r, s ∈ R; x, y ∈ R 1.2