Abstract
This chapter discusses fixed point iterations using infinite matrices. It presents an assumption as per which there is a normed linear space X; C is a nonempty, closed, bounded and convex subset of X; T: C → C is a mapping with at least one fixed point; and A is an infinite matrix. Given the iteration scheme x0 = x0 in C; xn+1 = Txn, n = 0, 1, 2 …, the chapter discusses the restriction on the matrix A that is necessary and/or sufficient to guarantee that the iteration scheme converges to a fixed point of T. Using these iteration schemes, results have been obtained for certain class of infinite matrices. This chapter presents the generalizations of several of these results. It presents a proof of a theorem for the solution of operator equations in a Banach space involving generalized contraction mappings and also presents a few results as corollaries.
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