Common fixed point theorems for a family multivalued mapping in Banach spaces
Zhanfei Zuo · 2011
Let K be a nonempty closed convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping Jφfor some gauge φ. Let Ti: K → K be a multivalued nonexpansive mappings with F := ∩i=0∞F(Ti) ≠ φ which is a sunny nonexpansive retract of K with Q a nonexpansive retraction. For a contraction f on K and {αn}, {βn} ϵ (0, 1), we consider the algorithm be called multivalued version of the modified Mann iteration xn+1= βnf(xn) + αnxn+ (1 - αn- βn)yn, where ynϵ Tnxnsuch that ∥yn+1- yn∥≤H(Tn+1xn+1, Tnxn).