Weak convergence theorems for infinite families of extended generalized hybrid mappings in Banach spaces
Journal of Nonlinear and Variational Analysis · 2019
Let E be a real Banach space and let C be a nonempty subset of E. A mapping T : C → E is said to be extended generalized hybrid if there are α, β , γ, δ ∈ R such that α + β + γ + δ ≥ 0, α + β > 0 and α T x -Ty 2 + β x -Ty 2 + γ T xy 2 + δ xy 2 ≤ 0 for all x, y ∈ C. In this paper, we prove a weak convergence theorem of Mann's type iteration for infinite families of extended generalized hybrid mappings in a Banach space satisfying the Opial's condition.