Coupled common best proximity point theorems for nonlinear contractions in partially ordered metric spaces

Existence of common best proximity point for single and multivalued non-self mappings

“…Suppose we have two non-self mappings f, g : A → B, the equations f x = x and gx = x are likely to have no common solution, known as common fixed point of the mappings f and g. In this situation, one wants to find approximate solution x such that the errors d(x, f x) and d(x, gx) are minimum for these two fixed point equations, called as common best proximity point of the mappings f and g. For detailed analysis on common best proximity point, we direct the reader to see [5,11,13,14,15,17,19].…”