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• Infimum problems derived from the proofs of some generalized Schwarz inequalities

  41-57

  Zoltán Boros

  Árpád Száz

  Views:

  63

  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

• Integral part problems derived from a solution of an in mum problem

  43-53

  Paweł Pasteczka

  Árpád Száz

  Views:

  17

  In this paper, we solve the following two integral part problems:
  Find all r ϵ R satisfying r^2 = [r]*([r]+1), resp. r^2≤[r]*([r]+1).
  These problems have been mainly motivated by a solution of an infimum problem of Z. Boros and Á. Száz.