We define f (a;b) (r) = ar + b/r for all a, b, r Є R with r > 0. And, for some subsets A of R, we determine F A_+ (a; b) = inf (r Є A_+) f (a,b) (r) ; where A_+ ={r Є A : r > 0}. The above in ma are mainly motivated by the proofs of some recent generalized Schwarz inequalities established by the present authors. Subject Classification: I35