[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2003.40.4.603

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)

Publication Information

Bulletin of the Korean Mathematical Society / v.40, no.4, 2003 , pp. 603-611 More about this Journal

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.

Keywords

K-positive definite operators; asymptotically K-positive definite operators; Frechet differentiable operators;

Citations & Related Records

Reference

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