Studies on Concave Young-Functions and Some Application to the Construction of Fixed Points of Real Functions

We succeeded to isolate a special class of concave Young-functions enjoying the so-called , which proves to be dense in the set of concave Young-functions. In this class there is a proper subset whose members have each the so-called degree of contraction (cf. ) denoted by , and map bijectively the interval [, ∞) onto itself. We construct the fixed point of each of these functions. Later we prove that every positive number is the fixed point of a concave Young-function having as degree of contraction. We then characterize those pairs () for which () = , where is an arbitrary real function and ∈ (−∞, ∞) \ {0}