OICC Press Communications in Nonlinear Analysis 2371-7920 6 1 2025 11 09 Optimal Coincidence Best Approximation Solution in b-fuzzy Metric Spaces EN Mujahid Abbas Department of Mathematics, Government College University,Lahore 54000, Pakistan. N. Saleem Department of Mathematics, University of Management and Technology, Lahore, Pakistan K. Sohail Department of Mathematics, Government College University,Lahore 54000, Pakistan. Journal Article 2025 11 09 In this paper, we prove the existence of optimal coincidence point and best proximity point in b-fuzzymetric space for two mappings satisfying certain contractive conditions and prove some proximal theoremswhich provide the existence of an optimal approximate solution to some operator equations which are notsolvable. We also provide an application to the fixed point theory of our obtained results.