Abstract
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.
Highlights
Let A be a normed space and G : D A → D, a mapping G is called nonexpansive ifGr − Ge r − e r, e D (1)Aoyama et al [8] presented a class of -hybrid mappings in a Hilbert space, meaning, a mapping G is called -hybrid ifGr − Ge 2 r − e 2 + 2(1− ) r − Gr, e − Ge (2)and showed a fixed point theorem
The concept of a monotone nonexpansive mapping is introduced by Bachar and Khamisi [10] in a POB space with the order “≾” and common approximate fixed points are realized of monotone nonexpansive semigroups
A mapping G : D A → D is said to be monotone nonexpansive if G is monotone (Gr ≾ Ge if r ≾ e) and
Summary
Let A be a normed space and G : D A → D , a mapping G is called nonexpansive if. During 2010-2020, Abed and Malih[19,20,21] established weak and strong convergence results of random Fibonacci-Mann and random Fibonacci-Ishikawa scheme to random fixed points of monotone random asymptotically nonexpansive mappings. Definition (1.5): [17] Let A be a Banach space satisfying Kadec-Klee property if for every sequence rn in A converging weakly to (r) together with rn converging strongly to r imply that rn converges strongly to a point r A. Lemma (1.7): [30] Let A be a reflexive Banach space, ∅ ≠D⸦A and A be a closed , assume that f : D → (− , ) is coercive and proper convex lower semi-continuous function. If rn and en weakly converges to r and e respectively, r ≾ e
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