By Aneke, Sylvanus Jude
This thesis consists of two parts. The first part deals with existerice and approximation techniques for finding solutions of operator equations or fixed points of operators belonging to certain classes of mappings. The classes of mappings studied include the K-posztz~~dee finzte operators, the suppressive mappings and accretive-type rntippings. In particular, it is proved that for a real
Banach space X, the equation Au = f , f E X, where A is a Kpd operator with the same domain as A', has a unique solution. An iteration process is constructed ant1 shown to converge strongly to the unique solution of this equation. Furtherniore, an asyrnptotzc version of Kpd operators is introduced and studied and a convergence result is proved. Drawing from the ideas of Alber