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.

in this paper, we give a concept of szl –widering mapping which is independent of nonspreading mappings, k – strictly pseudo nonspring mappings and nonexpansive mappings. Also we introduce a new proximal point schemes of resolvent and szl –widering mappings. On the other hand, we discuss that the weak and strong convergence for these proximal point schemes in real Hilbert space under different conditions to asymptotic common fixed point of szl –widering mappings.