A newly defined generalized metric space, called ₆-space and denoted by M₆= (, ₆), is introduced axiomatically and various ₆-concepts as ₆-fundamental sequence, ₆-convergence, ₆-contraction mapping, and ₆-fixed point are defined in the ₆-space, analogous to those in ₎-spaces. Thereafter, a generalized contraction mapping theorem called ₆-contraction mapping theorem is presented in the ₆-space, founding its statement and proof on these ₆-concepts. From the theorem, propositions concerning ₆-contraction mapping error estimates and the implication between ₎, ₆-spaces are derived. Then, a corollary concerning the implication between ₎, ₆-contraction mappings and the implication between ₎, ₆-fixed points are given. Finally, ₎, ₆-axioms and ₎, ₆-spaces are classified, an illustrative application is presented, highlighting some ₎, ₆-properties, and the work is concluded.
KHODABOCUS et al. (Sat,) studied this question.