Strong Convergence of a Multi-step Iterative Process for Relatively Quasi-nonexpansive Multivalued Mappings and Equilibrium Problem in Banach Spaces
نویسنده
چکیده
Let E be a real Banach space with norm ∥.∥ and let J be the normalized duality mapping from E into 2E ∗ given by Jx = {x∗ ∈ E∗ : ⟨x, x∗⟩ = ∥x∥∥x∗∥, ∥x∥ = ∥x∗∥} for all x ∈ E, where E∗ denotes the dual space of E and ⟨., .⟩ denotes the generalized duality pairing between E and E∗. A Banach space E is said to be strictly convex if ∥ 2 ∥ < 1 for all x, y ∈ E with ∥x∥ = ∥y∥ = 1 and x ̸= y. It is said to be uniformly convex if limn→∞ ∥xn−yn∥ = 0 for any two sequences {xn} and {yn} in E such that ∥xn∥ = ∥yn∥ = 1 and limn→∞ ∥nn 2 ∥ = 1. Let U = {x ∈ E : ∥x∥ = 1} be the unit sphere of E. Then the Banach space E is said to be smooth provided that
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