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Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup Ã¢Â„Â‘={T(s):sÃ¢Â‰Â¥0} with a common fixed point, a contraction f with coefficient 0<ÃŽÂ±<1, and a strongly positive linear bounded operator A with coefficient ÃŽÂ³Ã‚Â¯>0. Let 0<ÃŽÂ³<ÃŽÂ³Ã‚Â¯/ÃŽÂ±. It is proved that the sequence {xn} generated iteratively by xn=(IÃ¢ÂˆÂ’ÃŽÂ±nA)(1/tn)Ã¢ÂˆÂ«0tnT(s)ynds+ÃŽÂ±nÃŽÂ³f(xn),yn=(IÃ¢ÂˆÂ’ÃŽÂ²nA)xn+ÃŽÂ²nÃŽÂ³f(xn) converges strongly to a common fixed point xÃ¢ÂˆÂ—Ã¢ÂˆÂˆF(Ã¢Â„Â‘) which solves the variational inequality Ã¢ÂŒÂ©(ÃŽÂ³fÃ¢ÂˆÂ’A)xÃ¢ÂˆÂ—,zÃ¢ÂˆÂ’xÃ¢ÂˆÂ—Ã¢ÂŒÂªÃ¢Â‰Â¤0 for all zÃ¢ÂˆÂˆF(Ã¢Â„Â‘)

Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space