As it is not always true that the distance between points in fuzzy rectangular metric spaces one, so we introduce notions of and b-rectangular metric-like set theory generalize many existing results, which can be regarded as main advantage this paper. In these spaces, symmetry property preserved, but self may equal to one. We discuss topological properties demonstrate neither Hausdorff. Using α...

Let (M, ∂M) be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. We are interested in the following question: Question A Let h be a (non-smooth) metric on ∂M , with curvature K > −1. Is there a unique hyperbolic metric g on M , with convex boundary, such that the induced metric on ∂M is h ? There is also a dual statement: Question B Let h be a (non...

‎In this paper‎, ‎we introduce more general contractions called $varphi $-fixed‎ ‎point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $varphi $-‎fixed point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha‎‎)_{s}$-weak contractions in complete $b$-metric spaces‎. ‎Some examples are‎ ‎supplied to sup...