GOLDEN RATIO RIESZ-N ´AGY-TAK ´ACS DISTRIBUTION

Abstract

We study some properties of the Riemann-Stieltjes integrals with respect to the Riesz-N´agy-Tak´acs distribution Ha,p and its inverse Hp,a on the unit interval satisfying the equation 1 − a = a2 and p = 1 − a. Using the properties of the dual distributions Ha,p and Hp,a, we compare the Riemann-Stieltjes integrals of Ha,p over some essential intervals with that of its inverse Hp,a over the related intervals.

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