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

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).