Abstract
AbstractThe 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.
Highlights
Introduction and preliminariesIn, Bashirov et al, among other things, initiated a new kind of spaces, called multiplicative metric spaces (MMS for short)
For more details of this new kind of spaces the reader can refer to [, – ]. It follows from these papers that an MMS (X, d∗) is complete if and only if metric space (S-MS for short) (X, ln d∗) is such
MM d∗ and metric (SM for short) ln d∗ induce the same topology on X
Summary
Introduction and preliminariesIn , Bashirov et al, among other things, initiated a new kind of spaces, called multiplicative metric spaces (MMS for short). Let (X, d∗) be a complete MMS and let f be a self-mapping on X satisfying the following condition: for each ε > there exists δ > such that ε ≤ d∗(x, y) < ε · δ ⇒ d∗(fx, fy) < ε.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
