n this paper, we prove some common fixed point theorems for multivalued mappings and we present some new generalization contractive conditions under the condition of weak compatibility. our results extends chang-chen’s results  as well as ´ciri´c results. an example is given to support the usability of our results.

In this paper, we introduce the results of best proximity point in G-metric spaces for the cyclic contraction mapping with an example that illustrates the usability of the obtained results. 2010 AMS Subject Classification: 41A65, 46B85, 47H25.

We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g, we consider, for every n ≥ 1, a random quadrangulation qn uniformly distributed over the set of all rooted bipartite quadrangulations of genus g with n faces. We view it as a metric space by endowing its set of vertices with the graph distance. As n tends to infinity, this metric space, with distance...

Let (M, g) be an oriented 4-dimensional Riemannian manifold (not necessarily compact). Due to the Hodge-star operator ⋆, we have a decomposition of the bivector bundle ∧2 TM = ∧+ ⊕ ∧− . Here ∧± is the eigen-subbundle for the eigenvalue ±1 of ⋆. The metric g on M induces a metric, denoted by < , >, on the bundle ∧2 TM . Let π : Z = S (∧+) −→ M be the sphere bundle; the fiber over a point m ∈ M p...

Let l be a length function on a group G, and let Ml denote the operator of pointwise multiplication by l on l(G). Following Connes, Ml can be used as a “Dirac” operator for C ∗ r (G). It defines a Lipschitz seminorm on C∗ r (G), which defines a metric on the state space of C∗ r (G). We investigate whether the topology from this metric coincides with the weak-∗ topology (our definition of a “com...

We define the concept of a partial translation structure T on a metric space X and we show that there is a natural C *-algebra C * (T) associated with it which is a subalgebra of the uniform Roe algebra C * u (X). We introduce a coarse invariant of the metric which provides an obstruction to embedding the space in a group. When the space is sufficiently group-like, as determined by our invarian...

let (x, d) be a compact metric space and f : x → x be a continuous map. consider the metric space (k(x),h) of all non empty compact subsets of x endowed with the hausdorff metric induced by d. let ¯ f : k(x) → k(x) be defined by ¯ f(a) = {f(a) : a ∈ a} . we show that block-coppels chaos in f implies block-coppels chaos in ¯ f if f is a bijection.

The study of fixed points of mappings satisfying certain contractive conditions has been at the center of rigorous research activity, see 1–3 . The notion ofD-metric space is a generalization of usual metric spaces and it is introduced by Dhage 4–7 . Recently, Mustafa and Sims 8, 9 have shown that most of the results concerning Dhage’sD-metric spaces are invalid. In 8, 9 , they introduced an im...