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Fixed points for cyclic orbital generalized contractions on complete metric spaces
Authors:Erdal Karap?nar  Salvador Romaguera  Kenan Ta?
Institution:1. Department of Mathematics, At?l?m University, 06836, ?ncek, Ankara, Turkey
2. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022, Valencia, Spain
3. Department of Mathematics and Computer Science, ?ankaya University, 06530, Yuzuncuyil, Ankara, Turkey
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.
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