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Strong and weak convergence theorems for asymptotically nonexpansive mappings
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 nonexpansiveExpand
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Geometric Properties of Banach Spaces and Nonlinear Iterations
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
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Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings
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 realExpand
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Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings
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 anExpand
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Approximating fixed points of total asymptotically nonexpansive mappings
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. TheExpand
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Approximation of fixed points of strongly pseudocontractive mappings
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 intoExpand
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Fixed Point Iterations For Strictly Hemi-Contractive Maps In Uniformly Smooth Banach Spaces
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-contractiveExpand
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Convergence theorems for fixed points of uniformly continuous generalized Φ-hemi-contractive mappings
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
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Iterative Solution of Nonlinear Equations with Strongly Accretive Operators
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
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An example on the Mann iteration method for Lipschitz pseudocontractions
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.
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