The Farthest Orthogonality, Best Proximity Points and Remotest Points in Banach Spaces

In this paper, the concept of farthest orthogonality, distance orthogonality and $$*$$-farthest orthogonality in Banach spaces is introduced and the relation between these concepts with the dual space is found. Also, the weakly $$\phi $$-contraction and farthest continuous maps and their relationship are studied. Then, some best proximity and farthest point theorems are proved in Banach spaces. Some examples are given to illustrate the results.