Convergence and Stability of Iterative Scheme for a Monotone Total Asymptotically Non-expansive Mapping
Banach Space
Monotone Mappings
Total Asymptotically Non-expansive Mapping
Fixed Points
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.
