Extensions and applications of ACF mappings. (English) Zbl 1306.54043
Summary: Using a definition of ASF sequences derived from the definition of asymptotic contractions of the final type of ACF, we give some new fixed point theorem for cyclic mappings and an alternating mapping which extend results from T. Suzuki [J. Math. Anal. Appl. 335, No. 1, 707–715 (2007; Zbl 1128.54025), Theorem 2] and X. Zhang [J. Math. Anal. Appl. 333, No. 2, 780–786 (2007; Zbl 1133.54028), Theorem 1].
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 47H10 | Fixed-point theorems |
| 35A16 | Topological and monotonicity methods applied to PDEs |
References:
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| [2] | Di Bari, C.; Suzuki, T.; Vetro, C., Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 69, 11, 3790-3794 (2008) · Zbl 1169.54021 |
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| [6] | Suzuki, T., Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl., 253, 2, 440-458 (2001) · Zbl 0983.54034 |
| [7] | Suzuki, T., Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces, Nonlinear Anal., 64, 5, 971-978 (2006) · Zbl 1101.54047 |
| [8] | Suzuki, T., A definitive result on asymptotic contractions, J. Math. Anal. Appl., 335, 1, 707-715 (2007) · Zbl 1128.54025 |
| [9] | Suzuki, T., Asymptotic contractions of integral type, Bull. Kyushu Inst. Technol. Pure Appl. Math., 54, 1-11 (2007) · Zbl 1145.54046 |
| [10] | Zhang, X., Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl., 333, 2, 780-786 (2007) · Zbl 1133.54028 |
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