Beta-type functions and the harmonic mean

摘要

AbstractFor arbitrary$$f:left( a,infty ight) ightarrow left( 0,infty ight) ,$$f:a,∞→0,∞,$$age 0,$$a≥0,the bivariable function$$B_{f}:left( a,infty ight) ^{2}ightarrow left( 0,infty ight) ,$$Bf:a,∞2→0,∞,related to the Euler Beta function, is considered. It is proved that$$B_{fext { }}$$Bfis a mean iff it is the harmonic meanH. Some applications to the theory of iterative functional equations are given.]]>