A proof of the Generalized Banach Contraction Conjecture

A proof for a generalized Nakayama conjecture

In a recent paper Külshammer, Olsson, and Robinson proved a deep generalization of the Nakayama conjecture for symmetric groups. We provide a similar but a shorter and relatively elementary proof of their result. Our method enables us to obtain a more general H-analogue of the Nakayama conjecture where H is a set of positive integers.

A short proof of the maximum conjecture in CR dimension one

In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...

On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang’s Conjecture

The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...

A characterization of completeness of generalized metric spaces using generalized Banach contraction principle

In this paper, introducing a contraction principle on generalized metric spaces, a generalization of Banach’s fixed point theorem is obtained under the completeness condition of the space. Moreover, it is established that using such contraction principle completeness of the generalized metric space can be characterized.

A Geometrical Conjecture of Banach