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摘要
Let H be a real Hilbert space. Consider on H a nonexpansive semigroup S = {T(s) : 0 <= s < infinity} with a common fixed point, a contraction f with the coefficient 0 < alpha < 1, and a strongly positive linear bounded self-adjoint operator A with the coefficient <(gamma)over bar> > 0. Let 0 < gamma < (gamma) over bar/alpha. It is proved that the sequence {x(n)} generated by the iterative method x(0) is an element of H, x(n+1) = alpha(n)gamma f(x(n)) + beta(n)x(n) + ((1 - beta(n))I - alpha(n)A)(1/s(n)) integral(sn)(0) T(s)x(n)ds, n >= 0 converges strongly to a common fixed point x* is an element of F(S), where F(S) denotes the common fixed point of the nonexpansive semigroup. The point x* solves the variational inequality <(gamma f - A)x*, x - x*> <= 0 for all x is an element of F(S).
- 出版日期2012
- 单位杭州师范大学
