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


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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