Fixed point results in C^∗-algebra-valued metric spaces are direct consequences of their standard metric counterparts

Abstract

Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced (Formula presented.) -algebra-valued metric spaces as a new concept. Also, Ma and Jiang (Fixed Point Theory Appl. 2015:222, 2015), generalizing this concept, introduced (Formula presented.) -algebra-valued b-metric spaces. In both frameworks, these and other authors proved some fixed point results. We show in this paper that all these results (as well as many others) can be directly obtained as consequences of their standard metric or b-metric counterparts.