International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3955 2020 2020 Department of Psychological Counseling, College of Education for Human Sciences, University of Basrah, Iraq S. S. Tikrit University, College of Education for Pure Science, Department of Mathematics, Tikrit, Iraq Shadia Majeed noori Tikrit University, College of Education for Pure Science, Department of Mathematics, Tikrit, Iraq Yaseen, S.. R. Department of Mathematics, College of Science, University of Basrah, Basrah 61004, Iraq S. Khalil The present work explores the features of new kinds of neutrosophic continuous mappings, including neutrosophic irresolute β^*−continuous mapping (NIβ^*CM) and neutrosophic continuous mappings, including neutrosophic contra β^*−continuous mapping (NCOβ^*CM) and investigates some properties related them. Moreover, we study the relationships between these two concepts with the concept of irresolute α^* and contra α^*−continuous mapping. Finally, we introduced m-polar neutrosophic irresolute β^*−continuous mapping (MPNIβ^*CM) and neutrosophic continuous mappings, including m-polar neutrosophic contra β^*−continuous mapping (MPNCOβ^*CM) with investigates some properties related them. 2026 2026 01 09 10.54216/IJNS.270101 https://www.americaspg.com/articleinfo/21/show/3955