## “School of Mathematics”

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Paper   IPM / M / 15393
School of Mathematics
Title:   Approximate fixed points of α-nonexpansive mappings
Author(s):
 1 Alireza Amini-Harandi 2 Majid Fakhar 3 Hamid Reza Hajisharifi
Status:   Published
Journal: J. Math. Anal. Appl.
Vol.:  467
Year:  2018
Pages:   1168-1173
Supported by:  IPM
Abstract:
In this paper, we define the class of (Î±, Î²)-nonexpansive mappings which is properly larger than the class of Î±-nonexpansive mappings and prove that every (Î±, Î²)-nonexpansive mapping T:CâC has an approximate fixed point sequence, where Cis a nonempty bounded subset of a Banach space X, Î± >0and Î²â¥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 Î±-nonexpansive mappings, Ariza-Ruiz et al. (2016) [4].