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- Ya I Alber, C E Chidume, And H Zegeye
- 2006

We introduce a new class of asymptotically nonexpansive mappings and study approximating methods for finding their fixed points. We deal with the Krasnosel'skii-Mann-type iterative process. The strong and weak convergence results for self-mappings in normed spaces are presented. We also consider the asymptotically weakly contractive mappings.

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 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)

- C. E. Chidume, Bashir Ali, Donal O’Regan
- 2007

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)

- C. E. CHIDUME
- 2010

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)

Let E be a q-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., p, 1 < p < ∞). Let T be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset K of E and let ω ∈ K be arbitrary. Then the iteration sequence {zn} defined by z 0 ∈ K, z n+1 = (1 − µ n+1)ω + µ n+1 yn; yn = (1 − αn)zn… (More)

A new system of nonlinear fuzzy variational inclusions involving A, η-accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality inclusion problems as special cases of this system. By using the resolvent operator technique associated with A, η-accretive operator due to Lan et al. and… (More)

We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points… (More)