Some remarks on mappings satisfying cyclical contractive conditions
Tóm tắt
In this paper, we consider, discuss and complement fixed points results for mappings satisfying cyclical contractive conditions established by Kirk et al. (Fixed Point Theory 4(1):79–89, 2003). By using our new Lemma we get much shorter and nicer proofs of some results with the new concept of mappings.
Tài liệu tham khảo
Banach, S.: Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fund. Math. 3, 133–181 (1922)
Boyd, D.W., Wong, J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–464 (1969)
Caristi, J.: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241–251 (1976)
Edelstein, M.: On fixed and periodic points under-contractive mappings. J. London Math. Soc. 37, 74–79 (1962)
Geraghty, M.A.: On contractive mappings. Proc. Am. Math. Soc. 40, 604–608 (1973)
Kirk, W.A., Srinivasan, P.S., Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4(1), 79–89 (2003)