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| Paper IPM / M / 15393 |
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In this paper, we define the class of (α, β)-nonexpansive mappings which is properly larger than the class of α-nonexpansive mappings and prove that every (α, β)-nonexpansive mapping T:CâC has an approximate fixed point sequence, where Cis a nonempty bounded subset of a Banach space X, α >0and βâ¥0. This, in particular, gives an affirmative answer to the open question posed by Ariza-Ruiz and et al. concerning the existence of an approximate fixed point sequence for α-nonexpansive mappings, Ariza-Ruiz et al. (2016) [4].
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