Most Sequences derived from a family of non-expansive maps converges strongly to a fixed point of closed convex bounded subset of:Lp space, uniformly convex real Banach space with at least one of the maps being demi-compact and Hilbert spaces.The strong convergence of the sequences is achieved under certain mild conditions on some given parameters in a general Banach space.In these work we prove theorems on strong convergence of sequences with the conditions into considerations.These work gives an insight to a step by step approach to proves of theorems on convergences of sequences