A Generalization of Contraction Mapping Theorems in a Newly Defined Generalized Metric Space

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