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

[摘要] 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.

[关键词] Strictly J -pseudocontractive;J -Fixed point;Zeros of inverse strongly monotone map;Relatively weak J -nonexpansive map;2-Uniformly convex and uniformly smooth real Banach space