Best Proximity Point Theorems in Neutrosophic Complete Metric Spaces A. Sreelakshmi Unni1 , V. Pragadeeswarar1,∗ , Manuel De La Sen2 1Department of Mathematics, Amrita School of Physical Sciences Coimbatore, Amrita Vishwa Vidyapeetham, India 2 Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, 48940 Leioa, Bizkaia, Spain Emails: ua sreelakshmi@cb.students.amrita.edu; v pragadeeswarar@cb.amrita.edu; manuel.delasen@ehu.es Abstract In this work, we introduce the notion of best proximity point for a non-self map defined in a neutrosophic complete metric space. Moreover, we define the class of neutrosophic proximal contraction of first kind and second kind, and we prove theorems which ensures existence and uniqueness of best proximity point for such mappings in neutrosophic complete metric spaces. Additionally, a technique to identify an optimal approximation solution intended as a best proximity point is demonstrated. Keywords: Best proximity point; Neutrosophic complete metric space; Fixed point