Volume 27 • Issue 1 • PP: 206-219 • 2026
Best Proximity Point Theorems in Neutrosophic Complete Metric Spaces
View PDF 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
References
[1] L. A. Zadeh, Fuzzy sets, Information and control, vol.8, pp. 338–353, 1965.
[2] I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, vol.11, pp. 336–344, ´ 1975.
[3] Z. Deng, Fuzzy pseudo metric spaces, Journal of Mathematical Analysis and Applications, vol.86, pp. 74–95, 1982.
[4] O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy sets and systems, vol.12, pp. 215–229, 1984.
[5] B. Ali, M. Abbas, Fixed point theorems for multivalued contractive mappings in fuzzy metric spaces, American Journal of Applied Mathematics, vol.3, pp. 41–45, 2015.
[6] T. Dosenovic, D. Rakic, B. Caric, S. Radenovic, Multivalued generalizations of fixed point results in ´ fuzzy metric spaces, Nonlinear Analysis: Modelling and Control, vol.21, pp. 211–222, 2016.
[7] F. Kiany, A. Amini-Harandi, Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces, Fixed Point Theory and Applications, vol.2011, pp. 1–9, 2011.
[8] S. U. Rehman, H. Aydi, G. X. Chen, S. Jabeen, S. U. Khan, Some set-valued and multi-valued contraction results in fuzzy cone metric spaces, Journal of Inequalities and Applications, vol.2021, pp. 110, 2021.
[9] C. Vetro, P. Salimi, Best proximity point results in non-Archimedean fuzzy metric spaces, Fuzzy Information and Engineering, vol.5, pp. 417–429, 2013.
[10] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy sets and systems, vol.64, pp. 395–399, 1994.
[11] F. Smarandache, Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis, Rehoboth, NM: American Research Press, 1998.
[12] M. Kirisci, N. Simsek, Neutrosophic metric spaces, Mathematical Sciences, vol.14, pp. 241–248, 2020.
[13] S. Sowndrarajan, M. Jeyaraman, F. Smarandache, Fixed Point Results for Contraction Theorems in Neutrosophic Metric Spaces, Neutrosophic Sets and Systems, vol.36, pp. 1, 2020.
[14] U. Ishtiaq, D. A. Kattan, K. Ahmad, T. A. Lazar, V. L. Laz ´ ar, L. Guran, On intuitionistic fuzzy N b metric ´ space and related fixed point results with application to nonlinear fractional differential equations. Fractal and Fractional, vol.7, pp. 529, 2023.
[15] W. Shatanawi, K. Abodayeh, A. Mukheimer, Some fixed point theorems in extended b-metric spaces, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, vol.80, pp. 71–78, 2018.
[16] N. Alamgir, Q. Kiran, H. Aydi, A. Mukheimer, A Mizoguchi–Takahashi type fixed point theorem in complete extended b-metric spaces, Mathematics, vol.7, PP. 478, 2019.
[17] M. A. Al-Thagafi, Naseer Shahzad, Convergence and existence results for best proximity points, Nonlinear Analysis: Theory, Methods & Applications, vol.70, pp. 3665–3671, 2009.
Cite This Article
Choose your preferred format