General higher-order Lipschitz mappings. (English) Zbl 1480.47072
Summary: In this paper, we introduce a new class of mappings and investigate their fixed point property. In the first direction, we prove a fixed point theorem for general higher-order contraction mappings in a given metric space and finally prove an approximate fixed point property for general higher-order nonexpansive mappings in a Banach space.
MSC:
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
Keywords:
higher-order contraction mappings; metric space; approximate fixed point property; higher-order nonexpansive mappings; Banach spaceReferences:
| [1] | Goebel, K.; Japon-Pineda, M., A new type of nonexpansiveness, Proceedings of 8-th International Conference on Fixed Point Theory and Applications |
| [2] | Torrey, M., Fixed point results for a new mapping related to mean nonexpansive mappings, Advances in Operator Theory, 2, 1, 1-16 (2017) · Zbl 06692016 |
| [3] | Piasecki, Ł., Classification of Lipschitz Mappings (2013), Boca Raton, FL, USA: CRC Press, Boca Raton, FL, USA |
| [4] | Ezearn, J., Higher-order lipschitz mappings, Fixed Point Theory and Applications, 2015, 1, 88 (2015) · Zbl 1345.54043 · doi:10.1186/s13663-015-0334-1 |
| [5] | Gordon, J. F., The monotone contraction mapping theorem, Journal of Mathematics, 2020 (2020) · Zbl 1512.47078 · doi:10.1155/2020/2879283 |
| [6] | Aslantas, M.; Sahin, H.; Duran, T., Some caristi type fixed point theorems, The Journal of Analysis, 29, 1, 89-103 (2021) · Zbl 1460.54034 · doi:10.1007/s41478-020-00248-8 |
| [7] | Sahin, H.; Aslantas, M.; Altun, I., Feng-liu type approach to best proximity point results for multivalued mappings, Journal of Fixed Point Theory and Applications, 22, 1, 1-13 (2020) · Zbl 1431.54039 · doi:10.1007/s11784-019-0740-9 |
| [8] | Altun, I.; Aslantas, M.; Sahin, H., Best proximity point results for p-proximal contractions, Acta Mathematica Hungarica, 162, 2, 393-402 (2020) · Zbl 1474.54107 · doi:10.1007/s10474-020-01036-3 |
| [9] | Aslantas, M.; Sahin, H.; Altun, I., Best proximity point theorems for cyclic p-contractions with some consequences and applications, Nonlinear Analysis: Modelling and Control, 26, 1, 113-129 (2021) · Zbl 1476.54052 · doi:10.15388/namc.2021.26.21415 |
| [10] | Bernard, B.; Hermann, H., Rein analytischer beweis des lehrsatzes: dass zwischen je zwey werthen, die ein entgegengesetztes resultat gewähren, wenigstens eine reelle wurzel der gleichung liege, von bernard bolzano.-untersuchungen über die unendlich oft oszillierenden und unstetigen funktionen, von hermann hankel (1905), Ann Arbor, MI, USA: University of Michigan, Ann Arbor, MI, USA · JFM 37.0446.05 |
| [11] | Grabiner, D. J., Descartes’ rule of signs: another construction, The American Mathematical Monthly, 106, 9, 854-856 (1999) · Zbl 0980.12001 · doi:10.1080/00029890.1999.12005131 |
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