• Corpus ID: 31120914

CONVERGENCE THEOREMS FOR APPROXIMATION OF FIXED POINTS OF NONEXPANSIVE MAPPINGS IN BANACH SPACES

@inproceedings{Shehu2012CONVERGENCETF,
  title={CONVERGENCE THEOREMS FOR APPROXIMATION OF FIXED POINTS OF NONEXPANSIVE MAPPINGS IN BANACH SPACES},
  author={Yekini Shehu and Jeremiah Nkwegu Ezeora},
  year={2012}
}
Let E be a uniformly smooth and uniformly convex real Banach space and let K be a nonempty, closed and convex sunny nonexpansive retract of E with QK as the sunny nonexpansive retraction. Let T : K → K be a nonexpansive mapping such that F (T ) 6= ∅. Assume that either E admits weakly sequentially continuous duality mapping j or T is demicompact. Then, we introduce two approximation schemes (implicit and explicit) for finding a fixed point of a nonexpansive mapping and prove strong convergence… 

References

SHOWING 1-10 OF 12 REFERENCES

Weak Convergence Theorems for a Countable Family of Strict Pseudocontractions in Banach Spaces

We investigate the convergence of Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with the Fréchet differentiable norm. Our results

Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces

We introduce two iterative algorithms for nonexpansive mappings in Hilbert spaces. We prove that the proposed algorithms strongly converge to a fixed point of a nonexpansive mapping .

On deterministic convergence of iterations of relaxed projection operators

  • D. Youla
  • Mathematics
    J. Vis. Commun. Image Represent.
  • 1990

Iterative Approximation of Fixed Points

Pre-Requisites of Fixed Points.- The Picard Iteration.- The Krasnoselskij Iteration.- The Mann Iteration.- The Ishikawa Iteration.- Other Fixed Point Iteration Procedures.- Stability of Fixed Point

Image recovery by convex projections using a least-squares constraint

TLDR
A new convex constraint for image recovery using the method of projection onto convex sets is introduced and the resulting least-squares projection method is shown to provide improved performance over conventional projection techniques.

Nonlinear Functional Analysis

Iterative Algorithms for Nonlinear Operators

Iterative algorithms for nonexpansive mappings and maximal monotone operators are investigated. Strong convergence theorems are proved for nonexpansive mappings, including an improvement of a result

NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE.

  • F. Browder
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1965