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A general viscosity approximation method of fixed point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces

Somyot Plubtieng|Rattanaporn Wangkeeree
대한수학회 (The Korean Mathematical Society)|2008.11|대한수학회보 (Bulletin of the KMS)|제45권 제4호|pp. 717-728

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참고문헌

키워드

fixed pointstrong convergencenonexpansive semigroupviscosity approximationvariational inequality
주제분류수학

초록

Let H be a real Hilbert space and S = {T(s) : 0 ≤ s < ∞} be a nonexpansive semigroup on H such that F(S) ≠= 0. For a contraction f with coefficient 0 < α < 1, a strongly positive bounded linear operator A with coefficient [수식]. Let [수식]. It is proved that the sequences {xt} and {xn} generated by the iterative method [수식] and [수식] where {t}, {αn} ⊂ (0, 1) and {λt}, {tn} are positive real divergent sequences, converges strongly to a common fixed point x ∈ F(S) which solves the variational inequality <(γf − A)˜x, x − ˜x> ≤ 0 for x ∈ F(S).

Abstract

Let H be a real Hilbert space and S = {T(s) : 0 ≤ s < ∞} be a nonexpansive semigroup on H such that F(S) ≠= 0. For a contraction f with coefficient 0 < α < 1, a strongly positive bounded linear operator A with coefficient [수식]. Let [수식]. It is proved that the sequences {xt} and {xn} generated by the iterative method [수식] and [수식] where {t}, {αn} ⊂ (0, 1) and {λt}, {tn} are positive real divergent sequences, converges strongly to a common fixed point x ∈ F(S) which solves the variational inequality <(γf − A)˜x, x − ˜x> ≤ 0 for x ∈ F(S).

참고문헌 (17)

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