Strong Convergence Theorems for a Common Zero of an Infinite Family of Gamma-Inverse Strongly Monotone Maps with Applications
Charles Ejike Chidume, Ogonnaya Michael Romanus, and Ukamaka Victoria Nnyaba
African University of Science and
Let E be a uniformly convex and uniformly smooth real Banach space with
dual space E* and let Ak:E→E*,
k=1, 2, 3 , ...
be a family of inverse strongly monotone maps such that ∩∞k=1 Ak-1(0)≠∅.
A new iterative algorithm is constructed and proved to converge strongly to a common zero of the family.
As a consequence of this result, a strong convergence theorem for approximating a common J-fixed point for an infinite family of
gamma-strictly J-pseudocontractive maps is proved. These results are new and improve recent results obtained for these classes of nonlinear maps.
Furthermore, the technique of proof is of independent interest.
Full Text PDF: