Refinements of Results about Weighted Mixed Symmetric Means and Related Cauchy Means. (14th March 2011) - Horváth, László; Khan, Khuram Ali; Pečarić, J.
Abstract : A recent refinement of the classical discrete Jensen inequality is given by Horváth and Pečarić. In this paper, the corresponding weighted mixed symmetric means and Cauchy-type means are defined. We investigate the exponential convexity of some functions, study mean value theorems, and prove the monotonicity of the introduced means.