## ABSTRACT

This chapter considers a number of ways in which distance functions can be naturally introduced along with appropriate fixed-point theorem. It establishes corresponding fixed-point theorems analogous to the Banach contraction mapping theorem. The chapter deals with the different generalized metrics and corresponding fixed-point theorems for single-valued mappings. It examines the interconnections between the spaces underlying the various distance functions, and discusses a number of relevant examples. The chapter provides the tools needed for the application of distance functions in developing a unified approach to the fixed-point theory of very general and significant classes of logic programs. Relationships between gums and d-gums are studied, and the relationship between the Prieß-Crampe and Ribenboim theorem is investigated. The chapter discusses the multivalued mappings and some of the fixed-point theorems which are applicable to them. Not surprisingly, given their informal meaning, the formal meaning of disjunctive programs involves fixed points of multivalued mappings.