In this paper, we introduce the concept of contractive pair maps and give some necessary sufficient conditions for existence uniqueness best proximity points such pairs. our approach, have been weakened. An application has presented to demonstrate usability results. Also, cyclic ?-contraction asymptotic convergence theorems on point mappings. The results extend, generalize improve known from th...

In this paper, we present the notions of proximal contractions of Perov first and second kind and proximal cyclic contractions of Perov type and prove the existence and uniqueness of coincidence best proximity point under these contractive conditions in the frame work of regular cone metric space. Our results extend and generalized many existing results in literature.

For an embedding φ of the Cuntz algebra OM into ON , OM is identified with a subalgebra φ(OM) of ON . We construct irreducible representations of ON with continuous parameters by extending irreducible representations of OM . They are not unitarily equivalent to any generalized permutative representation, especially not to any permutative representation by Bratteli-Jorgensen and Davidson-Pitts. ...

Recent results have shown that any closed operator A commuting with the backwards shift S∗ restricted to K u := H 2 ⊖ uH, where u is an inner function, can be realized as a Nevanlinna function of S∗ u := S ∗| K2 u , A = φ(S∗ u), where φ belongs to a certain class of Nevanlinna functions which depend on u. In this paper this result is generalized to show that given any contraction T of class C0(...

We examine the problem of extending, in a natural way, order-preserving maps that are de ̄ned on the interior of a closed cone K1 (taking values in another closed cone K2 ) to the whole of K1 . We give conditions, in considerable generality (for cones in both ̄niteand in ̄nite-dimensional spaces), under which a natural extension exists and is continuous. We also give weaker conditions under which ...

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.