Some properties of a generalized Hamy symmetric function and its applications - Guan, Kaizhong; Guan, Ruke (Journal of mathematical analysis and applications, 2011)
This paper is concerned with the generalized Hamy symmetric function∑n(x,r;f)=∑1⩽i1<i2<⋯<ir⩽nf(∏j=1rxij1r), where f is a positive function defined in a subinterval of (0,+∞). Some properties, including Schur-convexity, geometric Schur-convexity and harmonic Schur-convexity are investigated. As applications, several inequalities are obtained, some of which extend the known ones.