Miklos Schweitzer 1977_8
Source: convex continuous functions
January 25, 2009
functionreal analysisreal analysis unsolved
Problem Statement
Let be a real number and \mathbb{R}_\plus{}\equal{}(0, \infty). For which continuous functions g : \mathbb{R}_\plus{} \rightarrow \mathbb{R}_\plus{} are following functions all convex? M_n(x)\equal{}\left[ \frac{\sum_{i\equal{}1}^n g(\frac{x_i}{x_{i\plus{}1}}) x_{i\plus{}1}^p}{\sum_{i\equal{}1}^n g(\frac{x_i}{x_{i\plus{}1}})} \right ]^\frac 1p , x\equal{}(x_1,\ldots, x_{n\plus{}1}) \in \mathbb{R}_\plus{} ^ {n\plus{}1} , \; n\equal{}1,2,\ldots
L. Losonczi