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Iterative solutions of K -positive definite operator equations in real uniformly smooth Banach spaces

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  • Zeqing Liu
  • Shin Min Kang
  • Jeong Sheok Ume

Abstract

Let X be a real uniformly smooth Banach space and let T : D ( T ) ⫅ X → X be a K -positive definite operator. Under suitable conditions we establish that the iterative method by Bai (1999) converges strongly to the unique solution of the equation T x = f , f ∈ X . The results presented in this paper generalize the corresponding results of Bai (1999), Chidume and Aneke (1993), and Chidume and Osilike (1997).

Suggested Citation

  • Zeqing Liu & Shin Min Kang & Jeong Sheok Ume, 2001. "Iterative solutions of K -positive definite operator equations in real uniformly smooth Banach spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:865439
    DOI: 10.1155/S0161171201005919
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