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Gabeleh, Moosa; Karimi, Lotfollah; Vetro, Calogero

Monotone orbitally nonexpansive and cyclic mappings in partially ordered uniformly convex Banach spaces. (English) Zbl 07880375

Iran. J. Math. Sci. Inform. 19, No. 1, 19-33 (2024).
Summary: In the setting of uniformly convex Banach spaces equipped with a partial order relation, we survey the existence of fixed points for monotone orbitally nonexpansive mappings. In this way, we extend and improve the main results of M. R. Alfuraidan and M. A. Khamsi [Proc. Am. Math. Soc. 146, No. 6, 2451–2456 (2018; Zbl 06852834)]. 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.

Cited in 1 Document

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces

Keywords:

best proximity point; \(T\)-cyclic contraction; monotone orbitally nonexpansive mapping; uniformly convex Banach space

Citations:

Zbl 06852834
Cite Review PDF
Full Text: DOI

References:

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[18] DOI: 10.61186/ijmsi.19.1.19 ] [ Downloaded from ijmsi.ir on 2024-05-28 ] Powered by TCPDF (www.tcpdf.org) · Zbl 07880375 · doi:10.61186/ijmsi.19.1.19
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