The Australian Journal of Mathematical Analysis and Applications


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ISSN 1449-5910  

 

Paper Information

Paper Title:

Strong Convergence Theorems for a Common Zero of an Infinite Family of Gamma-Inverse Strongly Monotone Maps with Applications

Author(s):

Charles Ejike Chidume, Ogonnaya Michael Romanus, and Ukamaka Victoria Nnyaba

African University of Science and Technology, Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng
E-mail: romanusogonnaya@gmail.com
E-mail: nnyabavictoriau@gmail.com

Abstract:

Let E be a uniformly convex and uniformly smooth real Banach space with dual space E* and let Ak:EE*, 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.

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