On multiplicative metric spaces: survey

Abstract

The purpose of this survey is to prove that the fixed point results for various multiplicative contractions are in fact equivalent to the corresponding fixed point results in (standard) metric spaces. For example, such are recent results established by He et al. (Fixed Point Theory Appl. 2014:48, 2014), Mongkolkeha and Sintunavarat (J. Nonlinear Sci. Appl. 8:1134-1140, 2015) and Abdou (J. Nonlinear Sci. Appl. 9:2347-2363, 2016) and all others from the list of references. Our results here generalize, complement, and improve recent ones from existing literature.