In the setting of uniformly convex Banach spaces equipped with a partially ordered relation, we survey the existence of fixed points for monotone orbitally nonexpansive mappings. In this way, we extend and improve the main results of Alfuraidan and Khamsi [M. R. Alfu-raidan, M. A. Khamsi, Proc. Amer. Math. Soc., 146, (2018), 2451-2456]. Examples are given to show the usability of our main conclusions. We also study the existence of an optimal solution for cyclic contractions in such spaces.
Gabeleh M., Karimi L., Vetro C. (2024). Monotone Orbitally Nonexpansive and Cyclic Mappings in Partially Ordered Uniformly Convex Banach Spaces. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS, 19(1), 19-33 [10.61186/ijmsi.19.1.19].
Monotone Orbitally Nonexpansive and Cyclic Mappings in Partially Ordered Uniformly Convex Banach Spaces
Vetro C.
2024-04-01
Abstract
In the setting of uniformly convex Banach spaces equipped with a partially ordered relation, we survey the existence of fixed points for monotone orbitally nonexpansive mappings. In this way, we extend and improve the main results of Alfuraidan and Khamsi [M. R. Alfu-raidan, M. A. Khamsi, Proc. Amer. Math. Soc., 146, (2018), 2451-2456]. Examples are given to show the usability of our main conclusions. We also study the existence of an optimal solution for cyclic contractions in such spaces.
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