Fuzzy gyronorms on gyrogroups

The concept of gyrogroups is a generalization groups which do not explicitly have associativity. In this paper, the notion fuzzy gyronorms on introduced. relations metrics (in sense George and Veeramani), are studied. Also, metric structures normed discussed. Finally completion gyrogroup with an invariant We mainly show that if d G (Gˆ,dˆ) space (G,d); then for any continuous t-norm ⁎, standard (Gˆ,Mdˆ,⁎) (up to isometry) unique (G,Md,⁎) furthermore, containing as dense subgyrogroup Mdˆ Gˆ. Applying result, we obtain every admits isometric) complete (G,d) such Gˆ topology introduced by dˆ topological