Generalized I-contractions , and R-subweakly Commuting Maps

  title={Generalized I-contractions , and R-subweakly Commuting Maps},
  author={Naseer Shahzad},
Let S be a subset of a normed space X = (X ,‖ · ‖) and T and I self-mappings of X . Then T is called (1) nonexpansive on S if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ S; (2) Inonexpansive on S if ‖Tx − Ty‖ ≤ ‖Ix − I y‖ for all x, y ∈ S; (3) I-contraction on S if there exists k ∈ [0,1) such that ‖Tx − Ty‖ ≤ k‖Ix − I y‖ for all x, y ∈ S. The set of fixed points of T (resp., I) is denoted by F(T) (resp., F(I)). The set S is called (4) pstarshaped with p ∈ S if for all x ∈ S, the segment [x, p] joining x… CONTINUE READING