The equivalence between the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mrow><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mi mathvariant="italic">S</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">T</mml:mi><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo linebreak="goodbreak" linebreakstyle="after">−</mml:mo></mml:mrow></mml:math> stabilities of Jungck-type iterative schemes

Akewe, Hudson; Olilima, Joshua; Eke, Kanayo Stella

doi:10.1016/j.heliyon.2021.e06368

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Definition 14 ([1]1

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2023

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“…Hence, we obtain that ∥T x − p∥ ∞ = 11 12 ∥x − p∥ ∞ , for every x ∈ l ∞ , p = 0. Thus, T satisfies contractive condition (6). But the map T is not a contraction.…”

Section: Definition 14 ([1]mentioning

confidence: 97%

Fixed point iterations for nonexpansive maps and their applications to constrained minimization and feasibility problems in Hilbert spaces

AKEWE,

Sawyerr,

Fasina

2023

Preprint

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The purpose of this study is to prove a faster iterative scheme than all of Thakur et al., Abbas and Nazir, Noor, Agarwal et al., Ishikawa, Picard-Mann, Mann and Picard iterations in the literature. The paper introduced three novel modified multistep iterative schemes (A), (B) and (C). Fixed point theorems are proven with these newly introduced multistep iterative schemes for the class of contraction mappings with fixed point p=Tp and nonexpansive mappings respectively. The rate of convergence was demonstrated numerically with the help of Python program and the results showed that our modified iterative scheme (C) converge in lesser number of iterations than existing iterative schemes in the literature. With the help of well constructed theorems, these modified multistep iterative schemes were applied to constrained minimization and split feasibility problems for the class of nonexpansive mappings in real Hilbert spaces.

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“…Hence, we obtain that ∥T x − p∥ ∞ = 11 12 ∥x − p∥ ∞ , for every x ∈ l ∞ , p = 0. Thus, T satisfies contractive condition (6). But the map T is not a contraction.…”

Section: Definition 14 ([1]mentioning

confidence: 97%

Fixed point iterations for nonexpansive maps and their applications to constrained minimization and feasibility problems in Hilbert spaces

AKEWE,

Sawyerr,

Fasina

2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

The equivalence between the (S,T)− stabilities of Jungck-type iterative schemes

Cited by 1 publication

References 9 publications

Fixed point iterations for nonexpansive maps and their applications to constrained minimization and feasibility problems in Hilbert spaces

Fixed point iterations for nonexpansive maps and their applications to constrained minimization and feasibility problems in Hilbert spaces

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