Existence, uniqueness and approximation of a solution for a K-positive definite operator equation

The notion of a K-positive definite (K pd) operator which has been studied for Hilbert spaces is extended to real separable strictly convex Banach spaces, X. For such an X, it is proved that the equation Au = f, f ε X, where A is a K pd operator with the same domain as K, has a unique solution. Furthermore, a strongly convergent iteration process is constructed. (author). 14 refs