Optimal solutions of minimization problems via new best proximity point results on quasi metric spaces

Abstract

In this paper, we prove some Boyd-Wong type best proximity point results in the setting of quasi metric spaces via Q-functions. First, we modify the fundamental concepts and notations in the best proximity point theory by taking into account unsymmetrical condition of quasi metric spaces. We provide some illustrative examples to examine our notations. Then, we introduce new concepts so called proximal BW-contraction and best BW-contraction mappings. Hence, we obtain best proximity point results for such mappings. Also, we give some nontrivial and comparative examples to show the effectiveness of our results. Next, we provide some corollaries and consequences to partial metric spaces of our main results. Finally, we present an existence and uniqueness result for nonlinear Volterra integral equations.