Naslov
Remarks on Gauss-Winckler's and Stolarsky's inequalities

Autori
Pečarić, Josip ; Varošanec, Sanja

Izvornik
Utilitas Mathematica (0315-3681) 48 (1995); 233-241

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Gauss-Winckler's inequality; Stolarsky's inequality; monotone function; absolute moment; convex function; concave function

Sažetak
K.B.Stolarsky proved the following result: If g is non-negative and non-increasing function on [0, 1], then for all positive numbers a and b we have: (a+b)g(0) \int_0^1 x^{; ; a+b-1}; ; g(x)dx \geq ab \int_0^1 x^{; ; a-1}; ; g(x)dx \int_0^1 x^{; ; b-1}; ; g(x)dx. In this paper we give simple connections between these results and the well-known Gauss-Winckler's inequality which states: Let Q:[0, \infty)->[0, 1] be a non-decreasing function such that Q(0)=0 and lim_{; ; x->\infty}; ; Q(x)=1. If Q' is continuous and non-increasing, then ((m+1)v_m)^1/m \leq ((r+1)v_r)^1/r for m\leq r, where v_m=\int_0^\infty x^m dQ(x).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA