Best proximity point theorems: An exploration of a common solution to approximation and optimization problems

Given a non-self mapping T:A→BT:A→B in the setting of a metric space, this work concentrates on the resolution of the non-linear programming problem of globally minimizing the real valued function x→d(x,Tx)x→d(x,Tx), thereby yielding an optimal approximate solution to the equation Tx=xTx=x. An iterative algorithm is also presented to compute a solution of such problems. As a sequel, it is possible to compute an optimal approximate solution to some non-linear equations.