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- W1984304966 abstract "Abstract. Let C be a nonempty closed convex subset of real Hilbertspace Hand F = fS(t) : t0ga nonexpansive self-mapping semigroupof C, and f: C!Cis a xed contractive mapping. Consider the processfx n g:(x n+1 = n x n + (1 n )z n z n = n f(x n ) + (1 n )S(t n )P C (x n r n Ax n ):It is shown that fx n gconverges strongly to a common element of the setof xed points of nonexpansive semigroups and the set of solutions of thevariational inequality for an inverse strongly-monotone mapping whichsolves some variational inequality. 1. IntroductionLet H be a real Hilbert space with inner product h;iand induced normkk, Cbe a nonempty closed convex subset of H. S: C!Cis nonexpansiveif kS(x) S(y)kkx yk;for all x;y2C. The set of xed points of SisF(S) = fx2C: x= Sxg. We assume that F(S) 6= ˚, it is well known thatF(S) is closed convex.A nonexpansive semigroup is a family F = fS(t) : t0gof self-mapping ofCif the following conditions are satis ed:(a) S(0)x= xfor all x2C;(b) S(s+ t) = S(s)S(t) for all s;t0;(c) For each t>0, kS(t)x S(t)ykkx yk;x;y2C:(d) For each x2C, the mapping S()xis continuous.In this paper, we use Fto denote the set of common xed points of F; that is,F= fx2C: S(t)x= x;t0g=" @default.
- W1984304966 created "2016-06-24" @default.
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- W1984304966 date "2012-11-30" @default.
- W1984304966 modified "2023-10-02" @default.
- W1984304966 title "VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE SEMINGROUPS AND MONOTONE MAPPPINGS" @default.
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- W1984304966 doi "https://doi.org/10.7858/eamj.2012.045" @default.
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