The paper refers to the Collatz's conjecture. In the first part, we present some equivalent
forms of this conjecture and a slight generalization of a former result from [1]. Then, we
present the notion of “chain subtrees” in Collatz's tree followed by a characterization
theorem and some subclass of numbers which are labels for some chain subtrees. Next, we
define the notion of “fixed points” and using this, we give another conjecture similar to
Collatz's conjecture. Some new infinite sets of numbers for which the Collatz's conjecture …

The paper refers to the Collatzs conjecture. In the first part, we present some equivalent
forms of this conjecture and a slight generalization of a former result from [1]. Then, we
present the notion of chain subtrees in Collatzs tree followed by a characterization theorem
and some subclass of numbers which are labels for some chain subtrees. Next, we define
the notion of fixed points and using this, we give another conjecture similar to Collatzs
conjecture. Some new infinite sets of numbers for which the Collatzs conjecture holds are …