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Strong and weak convergence theorems for asymptotically nonexpansive mappings

- C. E. Chidume, E. U. Ofoedu, H. Zegeye
- Mathematics
- 15 April 2003

Abstract Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T :K→E be an asymptotically nonexpansive… Expand

169 30- PDF

Geometric Properties of Banach Spaces and Nonlinear Iterations

- C. E. Chidume
- Mathematics
- 26 March 2009

1 Geometric properties. -1.1 Introduction. -1.2 Uniformly convex spaces. -1.3 Strictly convex Banach spaces. -1.4 The modulus of convexity. -1.5 Uniform convexity, strict convexity and reflexivity.… Expand

355 23

Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings

- C. E. Chidume
- Mathematics
- 1 February 1987

Suppose X = Lp (or lp), 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 {C, }?00 be a real… Expand

135 13- PDF

Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings

- C. E. Chidume, N. Shahzad
- Mathematics
- 1 September 2005

Abstract The purpose of this paper is to prove the strong convergence of an implicit iteration process to a common fixed point for a finite family of nonexpansive mappings. Our theorems give an… Expand

105 9

Approximating fixed points of total asymptotically nonexpansive mappings

- Y. Alber, C. E. Chidume, H. Zegeye
- Mathematics
- 2 March 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… Expand

86 9- PDF

Approximation of fixed points of strongly pseudocontractive mappings

- C. E. Chidume
- Mathematics
- 1 February 1994

Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Let T: K → K be a continuous strongly pseudocontractive mapping of K into… Expand

115 9- PDF

Fixed Point Iterations For Strictly Hemi-Contractive Maps In Uniformly Smooth Banach Spaces

- C. E. Chidume, M. Osilike
- Mathematics
- 1994

It is proved that the Mann iteration process converges strongly to the fixed point of a strictly hemi-contractive map in real uniformly smooth Banach spaces. The class of strictly hemi-contractive… Expand

62 8

Convergence theorems for fixed points of uniformly continuous generalized Φ-hemi-contractive mappings

- C. E. Chidume, C. O. Chidume
- Mathematics
- 15 March 2005

Abstract Let E be a real normed linear space, K be a nonempty subset of E and T : K → E be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., F ( T ) : = { x ∈ K : T x = x } ≠ Φ ,… Expand

50 7

Iterative Solution of Nonlinear Equations with Strongly Accretive Operators

- C. E. Chidume
- Mathematics
- 1 June 1995

Abstract Let E be a real Banach space with a uniformly convex dual. Suppose T : E → E is a strongly accretive map with bounded range such that for each ƒ ∈ E the equation Tx = ƒ has a solution in E .… Expand

75 7

An example on the Mann iteration method for Lipschitz pseudocontractions

- C. E. Chidume, S. Mutangadura
- Mathematics
- 18 January 2001

An example of a Lipschitz pseudocontractive map with a unique fixed point is constructed for which the Mann iteration sequence fails to converge. This resolves a long standing open problem.

212 6- PDF

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