Superquadratic method for generalized equations under relaxed conditions

Authors

  • I.K. Argyros Cameron University Department of Mathematics Sciences Lawton, OK 73505, USA.
  • S. Hilout Poitiers University Laboratoire de Mathematiques et Applications ´ Bd. Pierre et Marie Curie, Tel´ eport 2, B.P. 30179 ´ 86962 Futuroscope Chasseneuil Cedex, France.

Keywords:

Generalized equations, Banach space, center-Lipschitz condition, superquadratic method, set-valued map, ω-condition, variational inclusions, Frechet derivative, Aubin continuity

Abstract

We present a new approach to study the convergence of some superquadratic iterative method in Banach space for solving variational inclusions under different assumptions used in [12, 14, 2]. Here, we relax Lipschitz, Holder or center–H ¨ older type conditions by introducing ¨ ω–type–conditioned second order Frechet derivative. Under this condi- ´ tions, we show that the sequence is locally superquadratically convergent if some Aubin continuity property is satisfied. In particular, we recover a quadratic and a cubic convergence.

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Published

2013-12-31

Issue

Vol. 45 (2013)

Section

Articles

How to Cite

Superquadratic method for generalized equations under relaxed conditions. (2013). Punjab University Journal of Mathematics, 45(1), 1-7. https://pujm.pu.edu.pk/index.php/pujm/article/view/9