Approximation of a solution for a \(K\)-positive definite operator equation (Q1359646)

An iterative method is constructed which converges strongly to the unique solution of the equation \(Ax=f\) where \(A\) is a \(K\)-positive definite operator on a domain of a real separable \(q\)-uniformly smooth Banach space, \(q>1\). This class of Banach spaces includes the \(L_p\) (or \(\ell_p\)) spaces for \(1<p<+\infty\). The iterative process developed has been studied earlier for the case of Hilbert space. The result of the article is an extension of the similar result of \textit{C. E. Chidume} and \textit{S. J. Aneke} [Appl. Anal. 50, No. 3-4, 285-294 (1993; Zbl 0788.47051)] on the more general Banach spaces. Moreover, the weaker conditions were used instead of the commutativity assumption imposed in the mentioned article.