Certain dynamic iterative scheme families and multi-valued fixed point results

Ali, Amjad; Arshad, Muhammad; Emeer, Eskandar; Aydi, Hassen; Mukheimer, Aiman; Abodayeh, Kamaleldin

doi:10.3934/math.2022677

MATH

2022

DOI: 10.3934/math.2022677

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Certain dynamic iterative scheme families and multi-valued fixed point results

Amjad Ali

Muhammad Arshad

Eskandar Emeer

et al.

Abstract: <abstract><p>The article presents a systematic investigation of an extension of the developments concerning $ F $-contraction mappings which were proposed in 2012 by Wardowski. We develop the notion of $ F $-contractions to the case of non-linear ($ F $, $ F_{H} $)-dynamic-iterative scheme for Branciari Ćirić type-contractions and prove multi-valued fixed point results in controlled-metric spaces. An approximation of the dynamic-iterative scheme instead of the conventional Picard sequence is determ… Show more

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Cited by 3 publications

References 31 publications

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Fixed-point theorems of ${F}^{\star}- ( \psi,\phi )$ integral-type contractive conditions on $1_{E}$-complete multiplicative partial cone metric spaces over Banach algebras and applications

Faried,

Abou Bakr,

Abd El-Ghaffar

et al. 2023

J Inequal Appl

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In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on $1_{E}$ 1 E -complete multiplicative partial cone metric spaces over Banach algebras and formulate some existence and uniqueness results regarding the fixed-point theorems using some integrative conditions. Moreover, we validate the significance our results and exploit them to find the unique solution of a fractional nonlinear differential equation of Caputo type, which complements some previously well-known generalizations found in the literature.

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Fixed-point theorems of ${F}^{\star}- ( \psi,\phi )$ integral-type contractive conditions on $1_{E}$-complete multiplicative partial cone metric spaces over Banach algebras and applications

Faried,

Abou Bakr,

Abd El-Ghaffar

et al. 2023

J Inequal Appl

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show abstract

Certain New Development to the Orthogonal Binary Relations

et al. 2022

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In this study, inspired by the concept of B-metric-like space (BMLS), we introduce the concept of orthogonal B-metric-like space (OBMLS) via a hybrid pair of operators. Additionally, we establish the concept of orthogonal dynamic system (ODS) as a generalization of the dynamic system (DS), which improves the existing results for analysies such as those presented here. By applying this, some new refinements of the F⊥-Suzuki-type (F⊥-ST) fixed-point results are presented. These include some tangible instances, and applications in the field of nonlinear analysis are given to highlight the usability and validity of the theoretical results.

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Common fixed point results via $ \mathcal{A}_{\vartheta} $-$ \alpha $-contractions with a pair and two pairs of self-mappings in the frame of an extended quasi $ b $-metric space

Rezazgui

Tallafha

Shatanawi

2023

MATH

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<abstract><p>In this paper, we take advantage of implicit relationships to come up with a new concept called "$ \mathcal{A}_{\vartheta} $-$ \alpha $-contraction mapping". We utilized our new notion to formulate and prove some common fixed point theorems for two and four self-mappings over complete extended quasi $ b $-metric spaces under a set of conditions. Our main results widen and improve many existing results in the literature. To support our research, we present some examples as applications to our main findings.</p></abstract>

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Certain dynamic iterative scheme families and multi-valued fixed point results

Cited by 3 publications

References 31 publications

Fixed-point theorems of ${F}^{\star}- ( \psi,\phi )$ integral-type contractive conditions on $1_{E}$-complete multiplicative partial cone metric spaces over Banach algebras and applications

Fixed-point theorems of ${F}^{\star}- ( \psi,\phi )$ integral-type contractive conditions on $1_{E}$-complete multiplicative partial cone metric spaces over Banach algebras and applications

Certain New Development to the Orthogonal Binary Relations

Common fixed point results via $ \mathcal{A}_{\vartheta} $-$ \alpha $-contractions with a pair and two pairs of self-mappings in the frame of an extended quasi $ b $-metric space

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