Search Results

1 - 1 of 1 items :

  • "effective solvability" x
  • General Mathematics x
Clear All


Under some simple conditions on the real functions f and g defined on an interval I ⊂ (0, ), the two-place functions Af (x, y) = f (x) + y − f (y) and Gg(x,y)=g(x)g(y)y generalize, respectively, A and G, the classical weighted arithmetic and geometric means. In this note, basing on the invariance identity G ∘ (H, A) = G (equivalent to the Pythagorean harmony proportion), a suitable weighted extension Hf,g of the classical harmonic mean H is introduced. An open problem concerning the symmetry of Hf,g is proposed. As an application a method of effective solving of some functional equations involving means is presented.