Modified Iterative Algorithms for Nonexpansive Mappings
نویسندگان
چکیده
Let H be a real Hilbert space, let S, T be two nonexpansive mappings such that F S ∩ F T / ∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms for finding the approximate solution of two nonexpansive mappings as xn 1 βnxn 1 − βn Syn, yn αnγf xn I − αnA Txn, n ≥ 0, where γ > 0 is a real number and {αn}, {βn} are two sequences in 0, 1 satisfying the following control conditions: C1 limn→∞ αn 0, C3 0 < lim infn→∞ βn≤ lim supn→∞ βn < 1, then ‖xn 1 − xn‖ → 0. We also discuss several special cases of this iterative algorithm.
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