A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings
Tomonari Suzuki · Proceedings of the American Mathematical Society · 2006
In this paper, we prove a Halpern-type strong convergence theorem for nonexpansive mappings in a Banach space whose norm is uniformly Gâteaux differentiable. Also, we discuss the sufficient and necessary condition about this theorem. This is a partial answer of the problem raised by Reich in 1983.