On the quasi-derivation relation for multiple zeta values

Recently, Masanobu Kaneko introduced a conjecture on an extension of the derivation relation for multiple zeta values. The goal of the present paper is to present a proof of this conjecture by reducing it to a class of relations for multiple zeta values studied by Kawashima. In addition, some algebraic aspects of the quasi-derivation operator ${\mathrm{\partial }}_n^{(c)}$ on $$\mathbb{Q}$< x,y>$, which was defined by modeling a Hopf algebra developed by Connes and Moscovici, will be presented.