Let S : X → X be a nonexpansive mapping and suppose that F ( S ) ≠ ∅.
Let T : X → X be a nonexpansive mapping and suppose that F ( T ) ≠ ∅.
Theorem 2.1 Let A : E → E be a continuous mapping and suppose that the following two assertions hold.
Let F : X × X → X be a mapping, and suppose that F has the mixed monotone property.
Let T : X → X be a strongly quasinonexpansive and Δ-demiclosed mapping, and suppose that F ( T ) ≠ ∅.
Let T : A ∪ B → A ∪ B be a relatively nonexpansive mapping and suppose ( A, B ) has a proximal normal structure.
Theorem 3.1 Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map, and suppose that K ⊆ X is nonempty, bounded, closed, and convex.
Suppose that is a generalized nonexpansive mapping and a strongly generalized nonexpansive mapping, respectively, and suppose that For let the mapping be defined by (44).
Definition 8 Let { A i } i = 1 k be nonempty subsets of a metric space (X, d), let φ : ℝ+ → ℝ+ be a φ-mapping in X, and suppose f : ∪ i = 1 k A i → ∪ i = 1 k A i satisfies the following conditions (where A k+ 1 = A1): (i) f(A i ) ⊆ A i+ 1 for i = 1,2,...,k; (ii) d(fx, fy) ≤ φ (d x, y)) for all x ∈ A i, y ∈ A i+ 1, i = 1,2,...,k.
For k ∈ { 1, 2, 3, 4 }, let S k ˆ : X → F ( X ) be a fuzzy mapping satisfying condition and S k : X → CB ( X ) be a set-valued mapping induced by the fuzzy mapping S k ˆ, and suppose that S k is h-Lipschitz continuous with constants ξ k and that S 3 is γ-strongly accretive.
For k ∈ { 1, 2, 3, 4 }, let S k ˆ : X → F ( X ) be a fuzzy mapping satisfying condition and S k : X → CB ( X ) be a set-valued mapping induced by the fuzzy mapping S k ˆ, and suppose that S k is D-Lipschitz continuous with constants ξ k and that S 3 is γ-strongly accretive.
