Convergence and Stability of Iterative Scheme for a Monotone Total Asymptotically Non-expansive Mapping

SalwaSalwa Salman Abed; Athraa Najeb  Abed

doi:10.24996/ijs.2022.63.1.25

Authors

SalwaSalwa Salman Abed Department of Mathematics, College of Education for Pure Science Ibn Al Haitham, University of Baghdad, Iraq
Athraa Najeb Abed Department of Mathematics, College of Education for Pure Science Ibn Al Haitham, University of Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.1.25

Keywords:

Banach Space, Monotone Mappings, Total Asymptotically Non-expansive Mapping, Fixed Points

Abstract

In this work, we introduce Fibonacci– Halpern iterative scheme ( FH scheme) in partial ordered Banach space (POB space) for monotone total asymptotically non-expansive mapping (, MTAN mapping) that defined on weakly compact convex subset. We also discuss the results of weak and strong convergence for this scheme.

Throughout this work, compactness condition of m-th iterate of the mapping for some natural m is necessary to ensure strong convergence, while Opial's condition has been employed to show weak convergence. Stability of FH scheme is also studied. A numerical comparison is provided by an example to show that FH scheme is faster than Mann and Halpern iterative schemes.