More precisely, unless stated otherwise, in all later discussions, let Ω be a fixed, nonempty, closed and bounded domain in R m and let p : Ω → ( 0, ∞ ) be a fixed function which satisfies ∫ Ω p d ω = 1.
Let Ω be a fixed, nonempty, closed and bounded domain in R m, and let p = p ( X ) be the density function with support in Ω for the random vector X = ( x 1, x 2, …, x m ).
We assume that X is an arbitrarily fixed nonempty and bounded subset of the Banach algebra B C ( R + ), that is, X ∈ M B C ( R + ).
We also give conditions under which the set of fixed points turns out to be a nonempty CPO.
Lemma 2.4 [24] (Kakutani-Fan-Glicksberg fixed point theorem) Let X0 be a nonempty compact convex subset of X.
Let be a nonempty compact convex subset of a locally convex Hausdorff t.v.s.. Suppose that is half-continuous and for each, is nonempty, then has a fixed point.
Let E be a nonempty closed convex subset of a strictly convex Banach space X, let { t n : n ∈ N } be a family of single-valued nonexpansive mappings on E. Suppose ⋂ n = 1 ∞ Fix ( t n ) is nonempty.
Let C be a nonempty closed convex subset of a complete CAT ( 0 ) space X, let { t n : n ∈ N } be a family of single-valued nonexpansive mappings on C. Suppose ⋂ n = 1 ∞ Fix ( t n ) is nonempty.
Let C be a nonempty closed convex subset of a real Hilbert space H, and let S : C → C be a uniformly continuous asymptotically κ-strictly pseudocontractive mapping in the intermediate sense with sequence { γ n } such that Fix ( S ) is nonempty and bounded.
Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let S 1, S 2, … be nonexpansive mappings of C into itself such that ⋂ n = 1 ∞ Fix ( S n ) is nonempty, and let ξ 1, ξ 2, … be real numbers such that 0 < ξ i ≤ b < 1 for all i ≥ 1.
Let be a nonempty closed convex subset of a real Hilbert space and let be a sequence of -Lipschitzian mappings from into itself with. is said to satisfy the (SU) condition, if the following conditions hold: (1)for any strong convergence sequence, the sequence is also strong convergent; (2 the common fixed points set is nonempty; (3), where is defined by, for all, denotes the fixed points set of.
