in this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. meantime, an example is provided toillustrate this theorem. the main result shows that a self-mappingon a g-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. afterwards, some results inco...

Consider the following relaxation of the Hadwiger Conjecture: For each t there exists Nt such that every graph with no Kt minor admits a vertex partition into dαt + βe parts, such that each component of the subgraph induced by each part has at most Nt vertices. The Hadwiger Conjecture corresponds to the case α = 1, β = −1 and Nt = 1. Kawarabayashi and Mohar [K. Kawarabayashi, B. Mohar, A relaxe...

The problem of the holomorphic contractibility Teichmüller spaces T(0,n) punctured spheres (n>4) arose in 1970s connection with solving algebraic equations Banach algebras. Recently it was solved by author. In present paper, we give a refined proof for all T(0,n), n>4 and provide two independent proofs low-dimensional spaces, which has intrinsic interest.