Reduced Assumption in the Banach Contraction Principle‪.‬

Abstract: In this study we introduce a novel class of normed spaces called weakly Cauchy normed spaces not necessarily complete in general and proved the existence of a fixed point of contraction mappings in these spaces, this is weaker assumption than the completeness assumption imposed on the given normed space on the other side the contraction condition valid only on a closed convex subset of the given space. Key words: Reduced assumption, contraction mapping, Banach contraction principle, normed spaces