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Paper   IPM / M / 15173
School of Mathematics
  Title:   On generalized pointwise noncyclic contractions without proximal normal structure
  Author(s):  Moosa Gabeleh
  Status:   Published
  Journal: Ann. Funct. Anal.
  Year:  2018
  Pages:   DOI: 10.1215/20088752-2017-0049
  Supported by:  IPM
In this article, we introduce a new class of noncyclic mappings called generalized pointwise noncyclic contractions, and we prove a best proximity pair theorem for this class of noncyclic mappings in the setting of strictly convex Banach spaces. Our conclusions generalize a result due to Kirk and Royalty. We also study convergence of iterates of noncyclic contraction mappings in uniformly convex Banach spaces.

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