Abstract
In this paper, we introduce a general hybrid iterative method to find an infinite family of strict pseudo-contractions in a q-uniformly smooth and strictly convex Banach space. Moreover, we show that the sequence defined by the iterative method converges strongly to a common element of the set of fixed points, which is the unique solution of the variational inequality \(\left\langle {\left({\lambda \varphi - \nu {\cal F}} \right)\tilde z,{j_q}\left({z - \tilde z} \right)} \right\rangle \le 0\), for \(z \in \bigcap\limits_{i = 1}^\infty {\Gamma \left({{S_i}} \right)}\). The results introduced in our work extend to some corresponding theorems.
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This work was supported by the National Natural Science Foundation of China (12001416, 11771347 and 12031003), the Natural Science Foundations of Shaanxi Province (2021JQ-678).
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Wen, M., Li, H., Hu, C. et al. Iterative Methods for Obtaining an Infinite Family of Strict Pseudo-Contractions in Banach Spaces. Acta Math Sci 42, 1765–1778 (2022). https://doi.org/10.1007/s10473-022-0504-2
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DOI: https://doi.org/10.1007/s10473-022-0504-2