Weighted Power Means of Functions and Their Applications

By means of the concepts of the same order and the oppoite order between functions, studiedthe properties of weighted powr means of functions and their functional characteristics such as the loga-rithmic convexity and monotony when they are considered as functions of their power exponents. As appli-cations a new mean was introduced, comparisons between the so-called Holder's means and the Sto-larsky's means were made, and results of the refinements of the Ostle-Tewlliger inequality and of thearithmtic-geometric mean inequality were obtained.