Viscosity Approximation Method for Nonexpansive Nonself-mapping and Variational Inequality
نویسندگان
چکیده
Let E be a real reflexive Banach space which has uniformly Gâteaux differentiable norm. Let K be aclosed convex subset of E which is also a sunny nonexpansive retract of E, and T : K → E be nonexpansive mapping satisfying the weakly inward condition and F (T ) = {x ∈ K, Tx = x} 6= ∅, and f : K → K be a contractive mapping. Suppose that x0 ∈ K, {xn} is defined by { xn+1 = αnf(xn) + (1− αn)((1− δ)xn + δyn), yn = P (βnxn + (1− βn)Txn), n ≥ 0, where δ ∈ (0, 1), αn, βn ∈ [0, 1], P is sunny nonexpansive retractive from E into K. Under appropriate conditions, it is shown that {xn} converges strongly to a fixed point T and the fixed point solutes some variational inequalities. The results in this paper extend and improve the corresponding results of [2] and some others.
منابع مشابه
Iterative algorithms for families of variational inequalities fixed points and equilibrium problems
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