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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.
I.K. Argyros, S. Hilout. (2013) Superquadratic method for generalized equations under relaxed conditions, Punjab University Journal of Mathematics, Volume 45, Issue 1.
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