Asymptotic behavior of generalized nonexpansive sequences and mean points

Let E be a real Banach space with norm k-k and let fxngn, 0 be a generalized nonexpansive sequence in E (i.e. formula ommited where the series of nonnegative terms formula ommited is convergent). Let K = formula ommited We deal with the mean point of formula ommited concerning a Banach limit μ. If E is reflexive and d = d(0; K), then we show that formula ommited and there exists a pointformula ommited. In the sequel, this result is applied to obtain the weak and strong convergence of formula ommited.