New Iterative Algorithm for Two Infinite Families of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces

exists for each x, y ∈ S(E). In this case E is called smooth. The norm of E is said to be Fréchet differentiable if for each x ∈ S(E) the limit is attained uniformly for y ∈ S(E). The normofE is called uniformlyFréchet differentiable if the limit is attained uniformly for x, y ∈ S(E). It is well known that (uniform) Fréchet differentiability of the norm of E implies (uniform) Gâteaux differentiability of the norm of E. Let ρ E : [0,∞) → [0,∞) be the modulus of smoothness of E defined by