Krasnosel’skii Type Fixed Point Theorems for Mappings on Nonconvex Sets

نویسندگان

  • Maryam A. Alghamdi
  • Donal O’Regan
  • Naseer Shahzad
چکیده

and Applied Analysis3It is clear that every k-Lipschitz mapping is continuous. Moreover, the Banach contrac-tion principle holds for a closed subset in a complete p-normed space.Definition 2.2 see 3 . Let X, ‖ · ‖p 0 < p ≤ 1 be a p-normed space and 0 < s ≤ p. A setC ⊂ X is said to be s-convex if the following condition is satisfied1 − t x t1/sy ∈ C, whenever x, y ∈ C, t ∈ 0, 1 .2.2 Let A ⊂ X. The s-convex hull of A denoted by cosA is the smallest s-convex set containingA and the closed s-convex hull of A denoted by cosA is the smallest closed s-convex setcontaining A.In other words, the s-convexity of the set C is equivalent to thatt1x t2y ∈ C, whenever x, y ∈ C, t1, t2 ≥ 0,ts1 ts2 1.2.3 For s 1, we obtain the usual definition of convex sets. For a subsetA ofX, the s-convex hullof A is given by

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تاریخ انتشار 2014