This article devoted to present results on convergence of Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically αn-nonexpansive mapping (shortly, ma αn-n mapping) in partial ordered Banach space (shortly, POB space). Which are auxiliary theorem for demi-close's proof of this type of mappings, weakly convergence of increasing FFH-scheme to a fixed point with aid monotony of a norm and Σn+=∞1 λn= +∞, λn =min{hn , (1-hn)} where hn ⸦ (0,1) where is associated with FH-scheme for an integer n>0 more than that, convergence amounts to be strong by using Kadec-Klee property and finally, prove that this scheme is weak-w2 stable up on suitable status.
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.
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