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Minimum-Norm Fixed Point of Pseudocontractive Mappings

Author

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  • Habtu Zegeye
  • Naseer Shahzad
  • Mohammad Ali Alghamdi

Abstract

Let K be a closed convex subset of a real Hilbert space H and let be a continuous pseudocontractive mapping. Then for and each , there exists a sequence satisfying which converges strongly, as , to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.

Suggested Citation

  • Habtu Zegeye & Naseer Shahzad & Mohammad Ali Alghamdi, 2012. "Minimum-Norm Fixed Point of Pseudocontractive Mappings," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, September.
    • Handle: RePEc:hin:jnlaaa:926017
    DOI: 10.1155/2012/926017
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