Jong-Soo Jung

STRONG CONVERGENCE THEOREMS FOR LOCALLY PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z C such that ∥z-T(z)∥C, t[0, 1) defined by the equation z = tT(z)+(1-t)z is continuous and strongly converges to a fixed point of T as t longrightarrow 1￣.ow 1￣.