They proved that every weakly uniformly strict contraction on a complete metric space ((X,d)) has a unique fixed point.
In 1969, Meir and Keeler defined weak uniformly strict contraction as follows: given (epsilon>0), there exists (delta>0) such that epsilonle d x,y)< epsilon+deltaquad impliesquad d(Fx, Fy)< epsilon for a self-map F on X.
Meanwhile, Meir and Keeler [3] found that the conclusion of Banach's Theorem holds more generally from the following condition of a weakly uniformly strict contraction: Given (epsilon>0), there exists (delta>0) such that epsilonleq d x,y)< epsilon+deltaquad mbox{implies} quad d(Fx, Fy)< epsilon.
Let { V i : C → C } i = 1 ∞ be a countable family of uniformly k-strict pseudo-contractions.
A family of mappings { V i : C → H } i = 1 ∞ is called a family of uniformly k-strict pseudo-contractions, if there exists a constant k ∈ [0, 1) such that V i x - V i y 2 ≤ x - y 2 + k ( 1 - V i ) x - ( I - V i ) y 2, ∀ x, y ∈ C, ∀ i ≥ 1.
Let C be a nonempty closed convex subset of a real Hilbert Space H. Let { V i : C → C } i = 1 ∞ be a countable family of uniformly k-strict pseudo-contractions, { T i : C → C } i = 1 ∞ be a countable family of nonexpansive mappings defined by T i x = tx+(1 - t V i x, ∀x ∈ C, ∀i ≥ 1, t ∈ [k, 1). Suppose that Θ : = ∩ i = 1 ∞ F ( T i ) ≠ ∅.
Let { V i : C → C } i = 1 ∞ be a countable family of uniformly k-strict pseudo-contractions, { T i : C → C } i = 1 ∞ be a countable family of nonexpansive mappings defined by T i x = tx + (1 - t V i x, ∀x ∈ C, ∀i ≥ 1, t ∈ [k, 1). For l ∈ {1,2,..., M}, suppose Θ : = F ( S ) ∩ ( ∩ i = 1 ∞ F ( T i ) ) ∩ ( ∩ k = 1 N S M E P ( F k ) ) ∩ G S V I ( C, A l ) ≠ ∅.
The federal government is preparing to announce that the gray wolf, which was once nearly shot, trapped and poisoned out of existence in the lower 48 states, is abundant enough in a few places that it no longer uniformly needs the strict protection afforded the country's most endangered species.
A9 SCIENCE The Wolf's Endangered Status The federal government is preparing to announce that the gray wolf, which was once nearly shot, trapped and poisoned out of existence in the lower 48 states, is abundant enough in a few places in its range that it no longer uniformly needs the strict protection afforded the country's most endangered species.
Under mild conditions imposed on the parameter sequences { α n }, { β n } and { γ n }, we prove the strong convergence of { x n } to a common fixed point of a countable family { T n } of uniformly Lipschitz generalized strict pseudocontractions.
Since there are noise perturbations, the switching laws can not be exactly identified in a finite time horizon, we prove that if each individual subsystem is controllable and the switching duration uniformly has a strict positive lower bound, then the system can be stabilized by using on-line identification method and suitable designed controller.
