A short note on C ∗ $C^{*}$ -valued contraction mappings

Abstract

Abstract In this short note we point out that the recently announced notion, the C ∗ $C^{*}$ -valued metric, does not bring about a real extension in metric fixed point theory. Besides, fixed point results in the C ∗ $C^{*}$ -valued metric can be derived from the desired Banach mapping principle and its famous consecutive theorems.