Fixed points for cyclic orbital generalized contractions on complete metric spaces

Erdal Karapınar; Salvador Romaguera; Kenan Taş

Open Mathematics (2013)

  • Volume: 11, Issue: 3, page 552-560
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Erdal Karapınar, Salvador Romaguera, and Kenan Taş. "Fixed points for cyclic orbital generalized contractions on complete metric spaces." Open Mathematics 11.3 (2013): 552-560. <http://eudml.org/doc/269285>.

@article{ErdalKarapınar2013,
abstract = {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.},
author = {Erdal Karapınar, Salvador Romaguera, Kenan Taş},
journal = {Open Mathematics},
keywords = {Fixed point; Cyclic generalized contraction; Complete metric space; fixed point; cyclic generalized contraction; complete metric space},
language = {eng},
number = {3},
pages = {552-560},
title = {Fixed points for cyclic orbital generalized contractions on complete metric spaces},
url = {http://eudml.org/doc/269285},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Erdal Karapınar
AU - Salvador Romaguera
AU - Kenan Taş
TI - Fixed points for cyclic orbital generalized contractions on complete metric spaces
JO - Open Mathematics
PY - 2013
VL - 11
IS - 3
SP - 552
EP - 560
AB - 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.
LA - eng
KW - Fixed point; Cyclic generalized contraction; Complete metric space; fixed point; cyclic generalized contraction; complete metric space
UR - http://eudml.org/doc/269285
ER -

References

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