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

Abstract

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