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

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 scheme.
 Throughout compactness condition m-th iterate some natural m is necessary to ensure convergence, while Opial's has been employed show convergence. Stability studied. A numerical comparison provided by an example faster than Mann schemes.