Diameter estimation of gradient ?-Einstein solitons

The main aim of this article is to provide a lower bound the diameter compact gradient ?-Einstein soliton satisfying some given conditions. We have also deduced conditions with bounded Ricci curvature become non-shrinking and non-expanding. Further, we proved that complete non-compact shrinking or expanding Schouten non-constant potential along condition for boundedness scalar must be non-parabolic.