Generalized projection and approximation of fixed points of nonself maps

C. E. Chidume, M. Khumalo, H. Zegeye

Research output: Contribution to journalReview article

12 Citations (Scopus)

Abstract

Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T : K → E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T) := {x ε K: Tx = x} ≠ 0. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.

Original languageEnglish
Pages (from-to)242-252
Number of pages11
JournalJournal of Approximation Theory
Volume120
Issue number2
DOIs
Publication statusPublished - Feb 1 2003

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Generalized Projection
Banach spaces
Iterative methods
Fixed point
Perturbation
Uniformly Smooth Banach Space
Proper subset
Uniformly Convex
Approximation
Convergence Theorem
Rate of Convergence
Iteration
Closed
Operator
Estimate

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

Cite this

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Generalized projection and approximation of fixed points of nonself maps. / Chidume, C. E.; Khumalo, M.; Zegeye, H.

In: Journal of Approximation Theory, Vol. 120, No. 2, 01.02.2003, p. 242-252.

Research output: Contribution to journalReview article

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T1 - Generalized projection and approximation of fixed points of nonself maps

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AU - Khumalo, M.

AU - Zegeye, H.

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AB - Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T : K → E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T) := {x ε K: Tx = x} ≠ 0. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.

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