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- C E Chidume, Habtu Zegeye
- 2005

Let E be real Banach space which is both uniformly convex and uniformly smooth. Let T : D(T) C E —> E be bounded m-accretive operator, where the domain of T, D(T), is a proper subset of E. For a given f e E, an iterative method is constructed which converges strongly to the unique solution of the equation x + Tx = f. A related result deals with operator… (More)

- 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.

- C E Chidume, H Zegeye, Joseph A Ball
- 2003

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)

- C E Chidume, H Zegeye, Joseph A Ball
- 2004

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
- 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)

- C E Chidume, Jonathan M Borwein
- 2001

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)