Results on a faster iterative scheme for a generalized monotone asymptotically

Athraa Najeb Abed; Salwa Salman  Abed II

doi:10.24297/jam.v20i.9082

Authors

Athraa Najeb Abed Dep. Of Math. Colle. Of Education for Pure Sciences Ibn Al-Haitham University of Baghdad
Salwa Salman Abed II Department of Mathematics, college of Education for pure science Ibn Al Haitham,

DOI:

https://doi.org/10.24297/jam.v20i.9082

Keywords:

Banach space, fixed point, momotone mappings, α-nonexpansive mapping, iterative scheme

Abstract

This article devoted to present results on convergence of Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically α_n-nonexpansive mapping (shortly, ma α_n-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 Σ_n⁺₌^∞₁λ_n= +∞, λ_n=min{h_{n ,}(1-h_n)} where h_n⸦ (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.

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