In 2011, Gabeleh and Akhar [3] introduced semi-cyclic-contraction and considered the existence and convergence results of best proximity points in Banach spaces. In this paper, the author introduces a cone semicyclic φ-contraction pair in cone metric spaces and considers best proximity points for the pair in cone metric spaces. His results generalize the corresponding results in [1–5]..

This paper deals with the existence of an optimum solution a system ordinary differential equations via best proximity points. In order to obtain solution, we have developed point results for generalized multivalued contractions b-metric spaces. Examples are given illustrate main and show that new proper generalization some existing in literature.