We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal.
@article{bwmeta1.element.doi-10_2478_s11533-012-0145-0,
author = {Erdal Karap\i nar and Salvador Romaguera and Kenan Ta\c s},
title = {Fixed points for cyclic orbital generalized contractions on complete metric spaces},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {552-560},
zbl = {1281.54028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0145-0}
}
Erdal Karapınar; Salvador Romaguera; Kenan Taş. Fixed points for cyclic orbital generalized contractions on complete metric spaces. Open Mathematics, Tome 11 (2013) pp. 552-560. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0145-0/
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