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Displaying similar documents to “On mappings with contractive iterate at a point in generalized metric spaces.”

Multilinear operators on C ( K , X ) spaces

Ignacio Villanueva (2004)

Czechoslovak Mathematical Journal

Similarity:

Given Banach spaces  X , Y and a compact Hausdorff space  K , we use polymeasures to give necessary conditions for a multilinear operator from C ( K , X ) into  Y to be completely continuous (resp.  unconditionally converging). We deduce necessary and sufficient conditions for  X to have the Schur property (resp.  to contain no copy of  c 0 ), and for  K to be scattered. This extends results concerning linear operators.

On a quadratically convergent method using divided differences of order one under the gamma condition

Ioannis Argyros, Hongmin Ren (2008)

Open Mathematics

Similarity:

We re-examine a quadratically convergent method using divided differences of order one in order to approximate a locally unique solution of an equation in a Banach space setting [4, 5, 7]. Recently in [4, 5, 7], using Lipschitz conditions, and a Newton-Kantorovich type approach, we provided a local as well as a semilocal convergence analysis for this method which compares favorably to other methods using two function evaluations such as the Steffensen’s method [1, 3, 13]. Here, we provide...