New algorithms for approximating zeros of inverse strongly monotone maps and J-fixed points.

Let E be a real Banach space with dual space E ∗ . A new class of relatively weakJ-nonexpansive maps, T : E → E ∗ , is introduced and studied. An algorithm to approximate a common element of J-fixed points for a countable family of relatively weak J-nonexpansive maps and zeros of a countable family...

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Bibliographic Details
Published in:Fixed Point Theory & Applications Vol. 2020; no. 1; pp. 1 - 17
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Format: Article
Published: Springer Nature, 1/31/2020
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Summary:Let E be a real Banach space with dual space E ∗ . A new class of relatively weakJ-nonexpansive maps, T : E → E ∗ , is introduced and studied. An algorithm to approximate a common element of J-fixed points for a countable family of relatively weak J-nonexpansive maps and zeros of a countable family of inverse strongly monotone maps in a 2-uniformly convex and uniformly smooth real Banach space is constructed. Furthermore, assuming existence, the sequence of the algorithm is proved to converge strongly. Finally, a numerical example is given to illustrate the convergence of the sequence generated by the algorithm.