1. Fixed points for cyclic orbital generalized contractionson complete metric spaces
- Author
-
Kenan Taş, Salvador Romaguera, and Erdal Karapınar
- Subjects
Discrete mathematics ,Pure mathematics ,Cyclic generalized contraction ,General Mathematics ,Mathematics::General Topology ,Fixed-point theorem ,54e50 ,Fixed point ,Fixed-point property ,46t99 ,Complete metric space ,Metric space ,54h25 ,Schauder fixed point theorem ,QA1-939 ,Kakutani fixed-point theorem ,Brouwer fixed-point theorem ,MATEMATICA APLICADA ,47h10 ,Mathematics - 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, The authors are very grateful to the referee since his/her corrections and suggestions have fairly improved the first version of the paper. Salvador Romaguera also acknowledges the support of the Spanish Ministry of Science and Technology, grant MTM2009-12872-C02-01.
- Published
- 2013