In this paper, some discontinuity results are obtained using the number MC(t, t*) defined as MC(t,t*) = max { d(t,t*), ad(t,Tt) + (1-a)d(t*,St*), (1-a)d(t,Tt) ad(t*,St*), b/2 [d(t,St*) d(t*,Tt)]}, at common fixed point. Our provide a new and distinct solution to an open problem ?What contractive conditions which strong enough generate point but do not force map be continuous point?? given by Rh...

holds for all p, qEX (for all p, q with d(p, q) <e). Mappings, as above, satisfying (1) with the strict inequality sign for all p, qEX, pT^q (for all p, q with 0 <d(p, q) <e) are called contractive (e-contractive). A point yE Y EX is said to belong to the/-closure of Y, yE Y1, if /(F) C F and there is a point r¡E Y and a sequence {re,} of positive integers, («i<re2< • • ■ <Ui< ■ • ■ ), so that ...

Recent work has demonstrated that Clark’s theory of unitary perturbations of the backward shift restricted to a deBranges-Rovnyak subspace of Hardy space on the disk has a natural extension to the several variable setting. In the several variable case, the appropriate generalization of the Schur class of contractive analytic functions is the closed unit ball of the Drury-Arveson multiplier alge...

*Correspondence: [email protected] 4Department of Mathematics, Kyungnam University Masan, Kyungnam, 631-701, Korea Full list of author information is available at the end of the article Abstract A fixed point theorem is obtained for a monotone self-map in a 0-complete ordered partial metric space under Hardy-Rogers-type contractive condition. This result improves some recently obtained on...

The fixed point theorems in metric spaces are playing a major role to construct methods in mathematics to solve problems in applied mathematics and sciences. So the attraction of metric spaces to a large numbers of mathematicians is understandable. Some generalizations of the notion of a metric space have been proposed by some authors. In 2006, Mustafa in collaboration with Sims introduced a ne...

As an attempt to understand linear isometries between C∗-algebras without the surjectivity assumption, we study linear isometries between matrix algebras. Denote by Mm the algebra of m×m complex matrices. If k ≥ n and φ : Mn → Mk has the form X 7→ U [X ⊕ f(X)]V or X 7→ U [X t ⊕ f(X)]V for some unitary U, V ∈ Mk and contractive linear map f : Mn → Mk, then ‖φ(X)‖ = ‖X‖ for all X ∈ Mn. We prove t...

Environment-induced decoherence presents a great challenge to realizing a quantum computer. We point out the somewhat surprising fact that decoherence can be useful, indeed necessary, for practical quantum computation, in particular, for the effective erasure of quantum memory in order to initialize the state of the quantum computer. The essential point behind the deleter is that the environmen...