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The main purpose of this paper is to investigate the constrained extremal solution problem in Banach spaces in an abstract general setting.
Remark 1.1 It is worth to mention that the split common solution problem in Example 1.1 lies in two different subsets of the same space and the split common solution problem in Example 1.2 lies in two different subsets of the different space.
Though there exist several sufficient conditions of MP and AMP for the periodic solution problem in literature like [7 9] (for a brief explanation to these conditions, see Section 4.3), an optimal characterization on MP and AMP is not available.
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Some authors such as in references [1 7] presented various iterative schemes and showed some strong or weak convergence theorems on common solution problems in Hilbert spaces.
Hence, the maximum solution to the problem ) in is the maximum solution to the problem in.
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