On Ray's theorem for weak firmly nonexpansive mappings in Hilbert Spaces
DOI:
https://doi.org/10.24297/jam.v12i1.610Keywords:
generalized firmly nonexpansive mapping, fundamentally firmly nonexpansive mapping, fixed point, Hilbert space., Ray's theoremAbstract
In this work, we introduce notions of generalized firmly nonexpansive (G-firmly non expansive) and fundamentally firmly nonexpansive (F-firmly nonexpansive) mappings and utilize to the same to prove Ray's theorem for G-firmly and F-firmly nonexpansive mappings in Hilbert Spaces. Our results extend the result due to F. Kohsaka [ Ray's theorem revisited: a fixed point free firmly nonexpansive mapping in Hilbert spaces, Journal of Inequalities and Applications (2015) 2015:86 ].
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