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Paper   IPM / M / 15393
School of Mathematics
  Title:   Approximate fixed points of α-nonexpansive mappings
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
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:C→C has an approximate fixed point sequence, where Cis a nonempty bounded subset of a Banach space X, α >0and β≥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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