Resumen de Minkowski-type inequalities for means generated by two functions and a measure

László Losonczi, Zsolt Páles

• Given two continuous functions f; g : I ! R such that g is positive and f=g is strictly monotone, and a probability measure  on the Borel subsets of [0; 1], the two variable mean Mf;g; : I2 ! I is de ned by Mf;g;(x; y) := ( f g )..1 (�ç �ç 1 0 f ( tx + (1 .. t)y ) d(t) �ç �ç 1 0 g ( tx + (1 .. t)y ) d(t) ) (x; y 2 I):

  The aim of this paper is to study Minkowski-type inequalities for these means, i.e., to nd conditions for the generating functions f0; g0 : I0 ! R, f1; g1 : I1 ! R, . . . , fn; gn : In ! R, and for the measure  such that Mf0;g0;(x1 +
  
  
  + xn; y1 +
  
  
  + yn)  [] Mf1;g1;(x1; y1) +
  
  
  +Mfn;gn;(xn; yn) holds for all x1; y1 2 I1, . . . , xn; yn 2 In with x1 +
  
  
  + xn; y1 +
  
  
  + yn 2 I0.

  The particular case when the generating functions are power functions, i.e., when the means are generalized Gini means is also investigated.