2019Engineering and Technology JournalOpen access

Weak Convergence of Two Iteration Schemes in Banach Spaces

Salwa Salman Abed, Zahraa Mohamed Hasan

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Abstract

In this paper, we established weak convergence theorems by using appropriate conditions for approximating common fixed points and equivalence between the convergence of the Picard-Mann iteration scheme and Liu et al iteration scheme in Banach spaces. As well as, numerical examples are given to show that Picard-Mann is faster than Liu et al iteration schemes.

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What this paper is about

In this paper, we established weak convergence theorems by using appropriate conditions for approximating common fixed points and equivalence between the convergence of the Picard-Mann iteration scheme and Liu et al iteration scheme in Banach spaces. As well as, numerical examples are given to show that Picard-Mann is faster than Liu et al iteration schemes.

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Available abstract

In this paper, we established weak convergence theorems by using appropriate conditions for approximating common fixed points and equivalence between the convergence of the Picard-Mann iteration scheme and Liu et al iteration scheme in Banach spaces. As well as, numerical examples are given to show that Picard-Mann is faster than Liu et al iteration schemes.

Key concepts: Mathematics, Banach space, Fixed-point iteration, Convergence (economics), Equivalence (formal languages), Power iteration, Scheme (mathematics), Applied mathematics

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