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Iterative Methods for Obtaining an Infinite Family of Strict Pseudo-Contractions in Banach Spaces

Acta Mathematica Scientia(2022)

School of Mathematics and Information Science

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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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MKC,iterative algorithm,strict pseudo-contraction,β-Lipschitzian,δ-strongly monotone,Banach spaces
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