International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 3, Pages 155-160
doi:10.1155/S0161171201005919

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

Zeqing Liu,1 Shin Min Kang,2 and Jeong Sheok Ume3

1Department of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, China
2Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
3Department of Applied Mathematics, Ghangwon National University, Changwon 641-773, Korea

Received 2 October 2000

Copyright © 2001 Zeqing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 Tx=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).