Synchronal algorithm for a countable family of strict psedocontractions in q-uniformly smooth Banach spaces

Abstract

Let E be a real q-uniformly smooth Banach space whose duality map is weakly sequentially continuous and C be a nonempty, closed and convex subset of E. Let { Ti} ∞=1 : C → E be a family of k-strict pseudocontractions for k ∈ (0, 1) such that � ∞ i=1 F (Ti) � ∅, f be a contraction with coefficient β ∈ (0, 1) and { λi} ∞=1 be a real sequence in (0, 1) such that � ∞=1 λi = 1. Let G : C → E be an η-strongly accretive and L-Lipschitzian operator with L> 0, η> 0. Let { αn} and { βn} be sequences in (0, 1) satisfying some conditions. For some positive real numbers γ, µ appropriately chosen, let { xn} be a sequence de“ned by