Fixed Point Results in Orthogonal Neutrosophic Metric Spaces

Abstract

Neutrosophy deals with neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalization of the classical set, fuzzy set, and intuitionistic fuzzy set. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena, where it is necessary to study the relationship between two probability functions. In this study, the concept of an orthogonal neutrosophic metric space is initiated. It is a generalization of the neutrosophic metric space. Some fixed point results are investigated in this setting. For the validity of the obtained results, some nontrivial examples are given.

Solving Nonlinear Fractional Differential Equations for Contractive and Weakly Compatible Mappings in Neutrosophic Metric Spaces

“…Kiris ¸ci and Sims ¸ek [8] proposed the concept of neutrosophic metric space (NMS), based on the concept of NSs and proved several theorems in the proposed space. Ishtiaq et al [9] proposed the notion of orthogonal NMS and proved some fixed point results in the sense of complete orthogonal NMS. Several fixed point results for generalized contractions in NMS were demonstrated by Sowndrara et al [10].…”

Intuitionistic Fuzzy Double Controlled Metric Spaces and Related Results

“…Fuzzy metric space only discusses membership functions, so for dealing with membership and nonmembership functions, the notion of intuitionistic fuzzy metric spaces introduced by Park [5] and this concept was generalized into intuitionistic fuzzy bmetric spaces by Konwar [6]. In this connectedness, many important results appeared in the literature, such as fixed point theorems on intuitionistic fuzzy metric space [7], fixed point theorems for a generalized intuitionistic fuzzy contraction in intuitionistic fuzzy metric spaces [8], extension of fixed point results in intuitionistic fuzzy b-metric spaces [6], fixed points in intuitionistic fuzzy metric spaces [4], fuzzy fixed point [9], and some more work in generalized metric space in [10], ordered defined in fuzzy bmetric [11], partial metric defining the relation in [12], orthogonal neutrosophic metric space [13], and orthogonal partial metric space [14]. More details related to generalized metric spaces can be seen in [15].…”

On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

“…However, it does not mean that the results that are interesting from a mathematical point of view cannot be obtained using the NST formalism [12].…”