Neutrosophic Sets and Systems
Abstract
This study establishes fundamental results in the emerging domains of neutrosophic quadruple metric spaces and neutrosophic quadruple normed spaces. Building upon the recent definition of neutrosophic quadruple metric spaces, the first primary contribution is the development of fixed-point theory within this generalized framework. Specifically, we formulate and rigorously prove an analogue of the Banach contraction principle tailored for neutrosophic quadruple metric spaces. Furthermore, we establish additional fixed-point theorems applicable in this context, extending foundational results from classical metric spaces and simpler neutrosophic structures to handle the increased complexity and uncertainty modeled by quadruple-valued neutrosophic sets. The second major contribution involves the algebraic generalization of normed spaces. We introduce the novel concept of neutrosophic quadruple normed spaces. Within these spaces, we define an appropriate norm structure capable of measuring the "magnitude" of vectors characterized by quadruple-valued neutrosophic components. We systematically investigate and establish various fundamental properties of this newly defined norm, exploring concepts such as statistical convergence, Cauchy statistical convergence, boundedness, and continuity within the neutrosophic quadruple normed spaces. Additionally, we address the specific case of neutrosophic quadruple vector spaces, defining and analyzing the corresponding norm structure in this specialized context. The results generalize and extend prior work in fuzzy, intuitionistic fuzzy, and standard neutrosophic metric and normed spaces.
Recommended Citation
Şahin, Memet; Arif Sarıoğlan; and Amanzholova Alina Bolatkyzy. "Neutrosophic Quadruple Metric Spaces and Neutrosophic Quadruple Normed Spaces." Neutrosophic Sets and Systems 98, 1 (2026). https://digitalrepository.unm.edu/nss_journal/vol98/iss1/5