Let S be a surface with genus g and n boundary components and let d(S) = 3g − 3 + n denote the number of curves in any pants decomposition of S. We employ metric properties of the graph of pants decompositions CP(S) prove that the Weil-Petersson metric on Teichmüller space Teich(S) is Gromov-hyperbolic if and only if d(S) ≤ 2. When d(S) ≥ 3 the Weil-Petersson metric has higher rank in the sense...

‎in this paper‎, ‎generalized convex contractions on orthogonal metric spaces are stablished in whath might be called their definitive versions‎. ‎also, we show that‎ there are examples which show that our main theorems are genuine generalizations of theorem 3.1 and 3.2 of cite{r}‎[ m.a. miandaragh, m. postolache, s. rezapour, ‎textit{approximate fixed points of generalizedconvex contractions},...

A metric space is often represented as the pair (X,d). An example of metric spaces is (R, Lk), where Lk is the k-norm over R for given n, k ∈ Z≥1. We can represent a finite metric space (X, d) by a symmetric matrix S, of size nxn, where Si,j = d(i, j) and |X| = n. Metric spaces can be visualized using undirected graph G, where S is distance matrix for G. Conversely, given a graph G(V, E), we ca...

in this paper, we shall introduce the fuzzyw-distance, then prove a common fixed point theorem with respectto fuzzy w-distance for two mappings under the condition ofweakly compatible in complete fuzzy metric spaces.

we provide fuzzy quasi-metric versions of a fixed point theorem ofgregori and sapena for fuzzy contractive mappings in g-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.

in this paper is introduced a new type of generalization of metric spaces called sb metric space. for this new kind of spaces it has been proved a common xed point theorem for four mappings which satisfy generalized contractive condition. we also present example to conrm our theorem.

recently, phiangsungnoen et al. [j. inequal. appl. 2014:201 (2014)] studied fuzzy mappings in the framework of hausdorff fuzzy metric spaces.following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. an example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. finally, as an application of ou...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

in this paper, we prove the existence of fixed point for chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. the main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.