<abstract> <p>This manuscript is concerned for introducing novel concepts of <italic>ξ</italic>-chainable neutrosophic metric space and generalized neutrosophic cone metric spaces. We use four self-mappings to establish common fixed point theorem in the sense of <italic>ξ</italic>-chainable neutrosophic metric space and three self-mappings to establish common fixed point results in the sense of generalized neutrosophic metric spaces. Certain properties of <italic>ξ</italic>-chainable neutrosophic metric space and generalized neutrosophic metric spaces are defined and their examples are presented. An application to fuzzy Fredholm integral equation of second kind is developed to verify the validity of proposed results. These results boost the approaches of existing literature of fuzzy metric spaces and fuzzy fixed theory.</p> </abstract>

In this article, we establish the concept of intuitionistic fuzzy double-controlled metric-like spaces by “assuming that the self-distance may not be zero”; if the value of the metric is zero, then it has to be “a self-distance”. We derive numerous fixed-point results for contraction mappings. In addition, we provide several non-trivial examples with their graphical views and an application of integral equations to show the validity of the proposed results.

<abstract> <p>In this paper, we establish the concept of controlled neutrosophic metric-like spaces as a generalization of neutrosophic metric spaces and provide several non-trivial examples to show the spuriousness of the new concept in the existing literature. Furthermore, we prove several fixed point results for contraction mappings and provide the examples with their graphs to show the validity of the results. At the end of the manuscript, we establish an application to integral equations, in which we use the main result to find the solution of the integral equation.</p> </abstract>

Classical sets, fuzzy sets, intuitionistic fuzzy sets, and other sets are all generalized into the neutrosophic sets. A neutrosophic set is a mathematical approach that helps with challenges involving data that is inconsistent, indeterminate, or imprecise. The goal of this manuscript is to present the notion of neutrosophic 2-metric spaces. In this situation, we prove various fixed point theorems. The findings support previous methodologies in the literature and are backed up by various examples and an application.

In this manuscript, we establish the notion of neutrosophic b-metric spaces as a generalization of fuzzy b-metric spaces, intuitionistic fuzzy b-metric spaces and neutrosophic metric spaces in which three symmetric properties plays an important role for membership, non-membership and neutral functions as well we derive some common fixed point and coincident point results for contraction mappings. Also, we provide several non-trivial examples with graphical views of neutrosophic b-metric spaces and contraction mappings by using computational techniques. Our results are more generalized with respect to the existing ones in the literature. At the end of the paper, we provide an application to test the validity of the main result.