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This paper presents a nonlinear convergence algorithm for active dynamic undamped vibration absorber (ADUVA).
In Section 2, we gave a strong convergence algorithm for the problem (1.1).
A weak convergence algorithm and its special case are presented in Section 3.
Next, we introduce a strong convergence algorithm for the split common solution problem.
In this paper, we introduce a weak convergence algorithm and a strong convergence algorithm for the split common solution problem when the nonlinear operator T is a quasi-nonexpansive mapping.
It is easy to see that Algorithm 2 is not a modification of any weak convergence algorithm.
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Numerical experiments are also presented to illustrate the convergence algorithms.
In [1], the author established weak convergence algorithms and strong convergence algorithms for SEP (see [1] for more details).
As far as we know, most hybrid algorithms can be seen as the modification for weak convergence algorithms.
In the paper, we introduce a new hybrid algorithm which is not based on the modification to weak convergence algorithms.
Strong convergence algorithms for the split common solution problem for Lipschitzian accretive mappings and nonexpansive mappings (see Corollary 4.1 below).
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