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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, 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, 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
- 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)

- K R Kazmi, A Khaliq, A Raouf, C E Chidume, And H Zegeye, C.-X Huang +1 other
- 2007

In this paper, we consider a generalized mixed set-valued variational inequality problem which includes many important known variational inequality problems and equilibrium problem, and its related some auxiliary variational inequality problems. We prove the existence of solutions of the auxiliary variational inequality problems and suggest a two-step… (More)