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Let E be a real q-uniformly smooth Banach space with constant dq, q ≥ 2. Let T : E → E and G : E → E be a nonexpansive map and an η-strongly accretive map which is also κ-Lipschitzian, respectively. Let {λn} be a real sequence in 0, 1 that satisfies the following condition: C1: limλn 0 and ∑ λn ∞. For δ ∈ 0, qη/dqk 1/ q−1 and σ ∈ 0, 1 , define a sequence(More)
Let K be a nonempty closed convex subset of a real Banach space E and T be a Lipschitz pseudocontractive self-map of K with F (T) := {x ∈ K : T x = x} } = ∅. An iterative sequence {xn} is constructed for which ||xn − T xn|| → 0 as n → ∞. If, in addition, K is assumed to be bounded, this conclusion still holds without the requirement that F (T) = ∅.(More)
Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti : K → E, i = 1, . . . ,r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded(More)
Let H be a real Hilbert space. Let F : D(F) ⊆ H → H, K : D(K) ⊆ H → H be bounded monotone mappings with R(F) ⊆ D(K), where D(F) and D(K) are closed convex subsets of H satisfying certain conditions. Suppose the equation 0 = u + KF u has a solution in D(F). Then explicit iterative methods are constructed that converge strongly to such a solution. No(More)
and Applied Analysis 3 important, as has been observed by Bruck [18], mainly for the following two reasons. (i) Nonexpansive mappings are intimately connected with the monotonicity methods developed since the early 1960s and constitute one of the first classes of nonlinear mappings for which fixed point theorems were obtained by using the fine geometric(More)
Let E be a real Banach space, and K a closed convex nonempty subset of E. Let T1, T2, . . . , Tm : K → K bem total asymptotically nonexpansive mappings. A simple iterative sequence {xn}n≥1 is constructed inE and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti}i 1 are given. Furthermore, in the case that E is(More)
Recommended by Donal O'Regan Let E be a real Banach space, K a closed convex nonempty subset of E, and T 1 ,T 2 ,...,T m : K → K asymptotically quasi-nonexpansive mappings with sequences (resp.) {k in } ∞ n=1 satisfying k in → 1 as n → ∞, and ∞ n=1 (k in − 1) < ∞, i = 1,2,...,m. Let {α n } ∞ n=1 be a sequence in [, 1 − ], ∈ (0,1). Define a sequence {x n }(More)
Suppose X = Lp (or Ip), p > 2, and K is a nonempty closed convex bounded subset of X. Suppose T: K —* K is a Lipschitzian strictly pseudo-contractive mapping of K into itself. Let {Cn}^_0 be a real sequence satisfying: (i) 0 < C " < 1 for all n > 1, (") Z)rT=l Cn = °°> and Then the iteration process, zn G K, Zn+l = (1 — Cn)xn + CnTXn for n > 1, converges(More)
Suppose X is a real q-uniformly smooth Banach space and F,K : X → X with D(K) = F(X) = X are accretive maps. Under various continuity assumptions on F and K such that 0 = u+KFu has a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed on K and the operators K and F need not be(More)