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 Liu1
, Shin Min Kang2
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
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).