Site
www.artnet.com gives two artists with the name Rónai:
Dénes Rónai (1875-1964)
Géza Rónai (1886-1944)
Yes, Igor Guriev rights, there is Joseph Rippl-Ronai, but also "about" in Ronai written without accents.
Dénes Rónai was probably the photographer, but the artistic photos I could not find his other works.
But Géza Rónai, perhaps yours. He - a painter, on the Internet, you can look at his work. Signature also found (see picture). Generally - the Internet is a rich thing, if you make even a minimum of effort, then a lot can be found. Good Luck!
Few otfotoshopil you this signature. True, she works with pastels. In a letter to oil and may differ in detail.