On Cyclic Additivity Theorems

Remarks on Cyclic Additivity

On Best Proximity Point Theorems for New Cyclic Maps

In this paper, we first introduce the concept of MT − K condition. Some best proximity point theorems for mappings satisfying MT − K condition instead of K-cyclic mappings are established in metric spaces. Our results generalize and improve some main results in [5] and references therein. Mathematics Subject Classification: 54H25

Comments on Hastings’ Additivity Counterexamples

3 Background on random states and channels 7 3.1 Probability distributions for states . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Probability distributions on the simplex ∆d . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Estimates for μd,n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Probability distribution for random unitary channels . ....

Additivity and non-additivity for perverse signatures

A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifolds with boundary. Wall showed that this property is not true of signatures on...

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

and Applied Analysis 3 Df (y, x) − Df (x, y) = 2 (f (y) − f (x)) − ⟨y − x, f 󸀠 (x) + f 󸀠 (y)⟩ ,