RIO DE JANEIRO, Nov 26 (Reuters) - Controlling shareholders of Brazilian medical diagnostics company Alliar have accepted a takeover proposal by an investment fund linked to tycoon Nelson Tanure, the firm said in a Friday securities filing.

Alliar, formally Centro de Imagem Diagnosticos SA , said it had accepted an offer of 20.50 reais ($3.65) per share from MAM Asset Management Gestora de Recursos Ltd, implying a roughly 10% premium over the Friday closing price.

Tanure had previously offered 19 reais per share, but that takeover attempt was rejected in late October.

The businessman announced in August he had acquired a 26% stake in Alliar, saying he believed medical diagnostics was a promising sector in Brazil and that his daughter, a physician, had other investments in the industry.

($1 = 5.61 reais)

(Reporting by Gram Slattery Editing by Chris Reese)