A Study on p-Cyclic Orbital Geraghty type Contractions

Consider a metric space  and the non empty sub sets, of X. A map called p-cyclic orbital Geraghty type of contraction is introduced.  Convergence of a unique fixed point and a best proximity point for this map is obtained in a uniformly convex Banach space setting.  Also, this best proximity point is the unique periodic point of such a map.  </jats:p