Banach Contraction Mapping Theorem in (α, β, c)-Interpolative Metric Space

Abstract

In this paper we introduce the notion of (α, β, c)-interpolative metric space as an extension of (α, c)-interpolative metric space [Karapınar, E. (2023). An open discussion: Interpolative metric spaces. Advances in the Theory of Nonlinear Analysis and Its Applications, 7(5), 24-27]. The (α, β, c)-interpolative metric space can be regarded as a generalization of generalized metric space [Branciari, A. (2000). A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces.
Publicationes Mathematicae Debrecen, 57(1), 31-37]. Additionally, we prove the Banach contraction mapping theorem [Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales. Fundamenta Mathematicae, 3, 133-181] in (α, β, c)-interpolative metric space.