Let φ : Mn → B(H) be an injective, completely positive contraction with ‖φ−1 : φ(Mn) → Mn‖cb ≤ 1 + δ(ǫ). We show that if either (i) φ(Mn) is faithful modulo the compact operators or (ii) φ(Mn) approximately contains a rank 1 projection, then there is a complete order embedding ψ : Mn → B(H) with ‖φ − ψ‖cb < ǫ. We also give examples showing that such a perturbation does not exist in general. As ...

&lt;p&gt;The conceptions of &lt;em&gt;b&lt;/em&gt;-metric spaces and metric play a remarkable role in proving many theorems uniqueness existence solution such equations as integral or differential equations. The conception extended is considered generalization concept this was employed to unify some new fixed point results the literature. On other hand, simulation functions founded 2020 name ℋ-...

We prove the termination of 4-fold canonical flips. This paper is a supplement of [KMM, Theorem 5-1-15] and [M, Main Theorem 2.1]. We prove that a sequence of 4-fold log flips for canonical pairs terminates after finitely many steps. Let us recall the definition of canonical flips, which is slightly different from the usual one (cf. [S, (2.11) Adjoint Diagram]). Definition 1 (Canonical flip). L...

There are a lot of generalizations of the Banach contraction mapping principle in the literature. One of the most interesting of them is the result of Khan et al. 1 . They addressed a new category of fixed point problems for a single self-map with the help of a control function which they called an altering distance function. A function φ : 0,∞ → 0,∞ is called an altering distance function if φ...