Some extensions of Banach's contraction theorem

Abstract

The contraction theorem of Banac h remains the most fruitful means for proving and analyzing the convergence of iterative processes. For thi s reason, extension s of the theorem are of continuing interes t. The present paper describes '>ome extensions to a class of functions called local contrac tio ns . For comple te ness, we include he re a r esum e of the relevant defi nitions. A metric space (X, p) consists of a none mpty set X and a nonnegative-valued fun c tion p defined on X X X and satisfying