International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4107 2020 2020 Department of Mathematics, Amrita School of Physical Sciences Coimbatore, Amrita Vishwa Vidyapeetham, India V. V. Department of Mathematics, Amrita School of Physical Sciences Coimbatore, Amrita Vishwa Vidyapeetham, India V. Pragadeeswarar Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, 48940 Leioa, Bizkaia, Spain Manuel De La Sen 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. 2026 2026 206 219 10.54216/IJNS.270119 https://www.americaspg.com/articleinfo/21/show/4107