Some Borel measures associated with the generalized Collatz mapping

The Undecidability of the Generalized Collatz Problem

The Collatz problem, widely known as the 3x + 1 problem, asks whether or not a certain simple iterative process halts on all inputs. We build on earlier work by J. H. Conway, and show that a natural generalization of the Collatz problem is recursively undecidable.

Cauchy-Rassias Stability of linear Mappings in Banach Modules Associated with a Generalized Jensen Type Mapping

Some Natural Generalizations Of The Collatz Problem∗

We define here simple natural generalizations of Collatz Problem, stating some corresponding conjectures and showing some first interesting computations. We also address the conceptual importance of this kind of problems and the expected diffi culties into solving them. 1 Why Generalize an Apparently Intractable Problem? The Collatz Conjecture or 3x + 1 Conjecture, an elusive two-line algorithm...

Higher Derivations Associated with the Cauchy-Jensen Type Mapping

Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation 2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R) for all T,S,Rin K(H).

Higher Derivations Associated with the Cauchy-Jensen Type Mapping

Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation 2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R) for all T, S, R are in K(...