Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A LOCAL APPROXIMATION METHOD FOR THE SOLUTION OF K-POSITIVE DEFINITE OPERATOR EQUATIONS

  • Chidume, C.E. (Department of Mathematics, University of Nigeria) ;
  • Aneke, S.J. (Department of Mathematics, University of Nigeria)
  • Published : 2003.11.01
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Abstract

In this paper we extend the definition of K-positive definite operators from linear to Frechet differentiable operators. Under this setting, we derive from the inverse function theorem a local existence and approximation results corresponding to those of Theorems land 2 of the authors [8], in an arbitrary real Banach space. Furthermore, an asymptotically K-positive definite operator is introduced and a simplified iteration sequence which converges to the unique solution of an asymptotically K-positive definite operator equation is constructed.

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References

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  1. The Solution by Iteration of a Composed K-Positive Definite Operator Equation in a Banach Space vol.2010, 2010, https://doi.org/10.1155/2010/376852