We introduce a new property that we call the property (W.T). This property generalizes
and unifies the concept of noncompatible mappings due to Jungck (1986), the property (E.A)
of Aamri and Moutawakil (2002) and the concept of asymptotically regular maps due to
Browder and Petryshyn (1966). We use this concept to prove a general common fixed point
for two pairs of compatible maps under a contractive condition of Lipschitz type. We study
also the well-posedness of the fixed point problem for these maps. Our main result
extends, unifies and improves several recent results involving this Lipschitz type
condition which is is not a contractive condition of the classical type. So our work
provides some new contributions to the field of metric fixed point theory.
Publié le : 2011-01-15
Classification:
Common fixed point for four maps,
weakly compatible maps,
noncompatible maps,
property (E.A),
property (W.T),
Meir-Keeler type contractive condition,
Lipschitz type condition,
well-posedness,
54H25,
47H10
@article{1293054277,
author = {Akkouchi , Mohamed},
title = {On a Common Fixed Point Problem for Two Pairs of Maps Satisfying
the Property (W.T)},
journal = {Commun. Math. Anal.},
volume = {11},
number = {1},
year = {2011},
pages = { 111-120},
language = {en},
url = {http://dml.mathdoc.fr/item/1293054277}
}
Akkouchi , Mohamed. On a Common Fixed Point Problem for Two Pairs of Maps Satisfying
the Property (W.T). Commun. Math. Anal., Tome 11 (2011) no. 1, pp. 111-120. http://gdmltest.u-ga.fr/item/1293054277/