Unique common fixed points for four non-continuous mappings satisfying Ψ-implicit contractive condition on non-complete multiplicative metric spaces

Abstract

In this paper, we introduce a class Ψ of 5-dimensional real functions and consider a ψ-implicit contractive condition, and then discuss and obtain a unique common fixed point theorem for four non-continuous mappings defined on non-complete multiplicative metric spaces. Finally, we give several Ciric type fixed point theorems on non-complete multiplicative metric spaces.