A class of Newton maps with Julia sets of Lebesgue measure zero

Abstract Let $$g(z)=\int _0^zp(t)\exp (q(t))\,dt+c$$ g ( z ) = ∫ 0 p t exp q d + c where p , q are polynomials and $$c\in {\mathbb {C}}$$ ∈ C let f be the function from Newton’s method for g . We show that under suitable assumptions on zeros of $$g''$$ ′ Julia set has Lebesgue measure zero. Together with a theorem by Bergweiler, our result implies $$f^n(z)$$ f n converges to almost everywhere in $${\mathbb if this is case each zero not or $$g'$$ In order prove result, we establish general conditions ensuring sets have