Perov-fixed point theorems on a metric space equipped with ordered theoretic relation

Almalki, Yahya; Din, Fahim Ud; Din, Muhammad; Ali, Muhammad Usman; Jan, Noor

doi:10.3934/math.20221105

Cited by 8 publications

(8 citation statements)

References 11 publications

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“…Alam and Imdad introduced the idea of e-self-closedness for any R defined on some ( Ks , e), as elaborated in [15]. This concept was further elaborated by Almaliki et al in [25] as follows.…”

Section: Definition 5 ([25]) Assume a Binary Relation R Onmentioning

confidence: 99%

“…The concept of a path between two points within a set furnished with a binary relation in a vector-valued metric space was introduced by Almaliki et al in [25] as follows.…”

Section: Definition 7 ([15]mentioning

confidence: 99%

“…The notion of an improved vector-valued metric space using a binary relation was recently presented by Almalki et al [25]. They used the F-contraction in the context of a generalized metric space that has a binary connection to extend the Perov and Filip-Petrusel fixed-point theorems [26,27] to single-valued and multi-valued mappings.…”

Section: Introductionmentioning

confidence: 99%

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Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ-Contraction with Application to Nonlinear System of Matrix Equations

Din,

Alshaikey,

Ishtiaq

et al. 2024

Mathematics

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This paper combines the concept of an arbitrary binary connection with the widely recognized principle of θ-contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete vector-valued metric spaces. Through the utilization of binary relations and θ-contraction, this study advances and refines the Perov-type fixed-point results in the literature. Furthermore, this article furnishes examples to substantiate the validity of the presented results. Additionally, we establish an application for finding the existence of solutions to a system of matrix equations.

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Section: Definition 5 ([25]) Assume a Binary Relation R Onmentioning

confidence: 99%

“…The concept of a path between two points within a set furnished with a binary relation in a vector-valued metric space was introduced by Almaliki et al in [25] as follows.…”

Section: Definition 7 ([15]mentioning

confidence: 99%

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Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ-Contraction with Application to Nonlinear System of Matrix Equations

Din,

Alshaikey,

Ishtiaq

et al. 2024

Mathematics

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“…Hardy [7] established a generalization of Banach's theorem in a distinctive manner. Almalki et al [8] established some Perov-type results with theoretic order. Nazam et al [9] derived fixed points for a distinct category of contractions within partial b-metric spaces.…”

Section: Introductionmentioning

confidence: 99%

On Generalized Sehgal–Guseman-Like Contractions and Their Fixed-Point Results with Applications to Nonlinear Fractional Differential Equations and Boundary Value Problems for Homogeneous Transverse Bars

Din,

Ishtiaq,

Mukhtar

et al. 2024

Mathematics

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The goal of this study is to describe the class of modified Sehgal–Guseman-like contraction mappings and set up some fixed-point results in S-metric spaces. The class of generalized Sehgal–Guseman-like contraction mappings contains enhancements of Banach contractions, Kannan contractions, Chatterjee contractions, Chatterjee-type contractions, quasi-contractions, Ćirić–Reich–Rus-type contractions, Hardy–Rogers-type contractions, Reich-type contractions, interpolative Kannan contractions, interpolative Chatterjee contractions, among others, with their generalizations in S-metric spaces. We offer significant examples to substantiate the reliability of our results. This study also establishes consequential fixed-point results and applies them to nonlinear fractional differential equations and the boundary value problem for homogeneous transverse bars. At the end of the manuscript, we present an important open problem.

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“…In case 1, several so-called general metric spaces have been considered, such as: partial metric spaces, metric-like spaces, b-metric spaces, partial b-metric spaces and b-metric-like spaces (a total of six new different types of spaces, including metric spaces). For more details, see ( [2][3][4][5][6]).…”

mentioning

confidence: 99%

Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation”

Mitrovic

Fabiano

Radojević

et al. 2023

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Since 1964, when I.A. Perov introduced the so-called generalized metric space where d(x,y) is an element of the vector space Rm, many researchers have considered various contractive conditions in this type of space. In this paper, we generalize, extend and unify some of those established results. We are primarily concerned with examining the existence of a fixed point of some mapping from X to itself, but if (x,y) belongs to some relation R on the set X, then the binary relation R and some F contraction defined on the space cone Rm are combined. We start our consideration with the recently announced results and give them strict, critical remarks. In addition, we improve several announced results by weakening some of the given conditions.

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Perov-fixed point theorems on a metric space equipped with ordered theoretic relation

Cited by 8 publications

References 11 publications

Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ-Contraction with Application to Nonlinear System of Matrix Equations

Single and Multi-Valued Ordered-Theoretic Perov Fixed-Point Results for θ-Contraction with Application to Nonlinear System of Matrix Equations

On Generalized Sehgal–Guseman-Like Contractions and Their Fixed-Point Results with Applications to Nonlinear Fractional Differential Equations and Boundary Value Problems for Homogeneous Transverse Bars

Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation”

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