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

• Main Authors: Charles E. Chidume, Chinedu G. Ezea
• Format: Article
• Language: English
• Published: SpringerOpen 2020-01-01
• Series: Fixed Point Theory and Applications
• Subjects: 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
• Online Access: https://doi.org/10.1186/s13663-019-0668-1

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