From the abstract:<p>> In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.<p>That sounds like it's lacking some copy editing. So I'm not hopeful for the actual paper.<p>Also it doesn't look like this paper actually proves the Collatz Conjecture? It ends with:<p>> Unfortunately, the conditions of the theorem 2.3 are not satisfied in other cases.<p>> Furthermore, since N is discrete, Theorem 2.2 is sufficient without using Theorem 2.3, however, the conditions of the theorem 2.2 are also not satisfied.<p>And nothing more concrete.