  The aim of this paper is to address an open problem given in [Kirk, W. A.,
Shahzad, Naseer, Normal structure and orbital fixed point conditions, J. Math.
Anal. Appl. {\bf{vol 463(2)}}, (2018) 461--476]. We give a characterization of
weak proximal normal structure using best proximity pair property. We also
introduce a notion of pointwise cyclic contraction wrt orbits and therein prove
the existence of a best proximity pair in the setting of reflexive Banach
spaces.
