New Classes of δ − β∗-Continuous Mappings in m-Polar Neutrosophic Topological Spaces

We introduce and study two classes of neutrosophic continuous mappings: the neutrosophic irresolute δ−β∗-continuous mappings (NIr δ−β∗ CM) and the neutrosophic contra δ−β∗-continuous mappings (NC δ−β∗ CM). We establish their fundamental properties and provide characterizations in terms of preimages of δ−β∗-open and δ−β∗-closed sets. The interplay between the two notions is analyzed through implication chains, (non-)equivalences under mild hypotheses, and stability results under composition, subspaces, and products. We then extend the framework to the m-polar setting by defining m-polar neutrosophic irresolute δ−β∗-continuous mappings (MPNIr δ−β∗ CM) and m-polar neutrosophic contra δ−β∗-continuous mappings (MPNC δ−β∗ CM), showing how core properties lift to the m-polar case and where genuinely new phenomena arise. Throughout, examples and counterexamples are provided to separate the classes and to illustrate the sharpness of the obtained results.