2.1) To investigate the significance of some geometric properties. For examples, the existence of the best proximity points for extending and generalizing the class of proximal contraction under some conditions related to some geometric properties.
2.2) To establish new algorithm for approximating global solution to the best proximity points of mappings which related to the convex minimization problems and optimization problems.
2.3) To obtain couple (common) best proximity point theorems without some conditions in some metric spaces and for set-valued non-self maps.
2.4) To establish the existence of common best proximity points; iterative algorithms are also furnished to determine such optimal approximate solutions.
2.5) To resolve an optimization problem in the setting of a metric space that is endowed with a partial order.
2.6) Study the existence of solutions for the minimization problem min_x?A ||x ?T x||
