Let E be a real Banach space with dual space $E^{*}$. A new class of relatively weakJ-nonexpansive maps, $T:E\rightarrow E^{*}$, 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.

中文翻译：

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逼近强单调逆图和J固定点的零点的新算法

令E为具有双重空间$ E ^ {*} $的真实Banach空间。引入并研究了一类新的相对较弱的J非扩张映射$ T：E \ rightarrow E ^ {*} $。构造了一种算法，该算法为2个均匀凸且均匀光滑的实际Banach空间中的一个相对较弱的J-非扩张映射的可数族和一个可计数的逆强单调映射族的零来逼近J-定点的公共元素。此外，假设存在，则证明该算法的序列收敛性强。最后，给出了一个数值例子来说明该算法生成的序列的收敛性。