Abstract
Our aim is to define a new mean having specific properties which are crucial in several applications. As examples of this kind of applications, we can mention subdivision and multiresolution schemes based on nonuniform meshes and the numerical solution of conservation laws. Specifically, we pay attention to three relevant properties: to remain close to the minimum of the two values, to give a closer value to the weighted arithmetic mean of the two values when they are already similar, and to accomplish a Lipchitz condition. We define a family of means depending on a parameter k that matches these requirements. Using these means, it is possible to obtain more accurate theoretical constants in some stability theorems, and therefore they are better fitted to what happens in real examples. We carry out examples in the fields of subdivision schemes and hyperbolic conservation laws.
Disclosure statement
No potential conflict of interest was reported by the author(s).