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A-monotone nonlinear relaxed cocoercive variational inclusions

100%

Verma R.

Open Mathematics

2007

tom 5

nr 2

386-396

Based on the notion of A - monotonicity, a new class of nonlinear variational inclusion problems is presented. Since A - monotonicity generalizes H - monotonicity (and in turn, generalizes maximal monotonicity), results thus obtained, are general in nature.

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

68%

Argyros I., Ren H.

Open Mathematics

2008

tom 6

nr 2

262-271

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 an analysis of this method under the gamma condition [6, 7, 19, 20]. In particular, we also show the quadratic convergence of this method. Numerical examples further validating the theoretical results are also provided.

Ograniczanie wyników

2 Open Mathematics

1 Argyros I.

1 Ren H.

1 Verma R.

1 2008

1 2007

Wyniki wyszukiwania

A-monotone nonlinear relaxed cocoercive variational inclusions

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