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

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).