Common fixed point theorem for two commutative mappings involving iterates
DOI:
https://doi.org/10.66147/lnaa.20264491Keywords:
Common fixed point, commutative mappings, nonexpansive mappings, Hilbert spaceAbstract
We establish a common fixed point theorem for two commutative mappings in a real Hilbert space under a joint condition involving both mappings and their iterates. Our condition directly describes the interaction between the two mappings and generalizes a condition involving the two mappings separately. The main theorem guarantees the existence of a common fixed point under a boundedness assumption on the common orbit. As special cases, we obtain a previously known common fixed point theorem and, in particular, the common fixed point theorem for two commutative nonexpansive mappings. Examples illustrating the applicability of the theorem are also presented.
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Copyright (c) 2026 Atsumasa Kondo
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