In this paper, we introduce the concepts of the modified weak \(P_{\rho }\) -property and Suzuki type \(F_{\alpha ,\rho }\) -contraction mapping on quasi metric spaces. Then, we prove some left and right best proximity point results for such mappings on quasi metric spaces. Hence, we give an affirmative answer to the question in Altun (Journal of Nonlinear and Convex Analysis 16(4):659-666, 2015) for closed and bounded valued mappings. Also, we provide some comparative examples to show the effectiveness of the results in the current paper. Finally, we obtain a best proximity point result for the homotopic mappings by using our results.
