New algorithms for approximating zeros of inverse strongly monotone maps and J-fixed points
C.E. Chidume, Chinedu G. Ezea · Fixed Point Theory and Applications · 2020
Abstract LetEbe a real Banach space with dual space $E^{*}$ E∗ . A new class ofrelatively weakJ-nonexpansive maps, $T:E\rightarrow E^{*}$ T:E→E∗ , is introduced and studied. An algorithm to approximate a common element ofJ-fixed points for a countable family of relatively weakJ-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.