Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators

Hammad, Hasanen A.; Elmursi, Mohamed; Rashwan, Rashwan A.; Işık, Hüseyin

doi:10.1186/s13662-022-03724-6

Cited by 4 publications

(1 citation statement)

References 22 publications

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“…Anevska et al [5] provided proofs for some fixed-point results in 2-Banach spaces. Hammad [6] formulated fixed-point methodologies to address a category of matrix difference equations associated with a novel collection of contractions. Hardy [7] established a generalization of Banach's theorem in a distinctive manner.…”

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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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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Existence of Positive Solutions for a Singular Hessian Equation with a Negative Augmented Term

Zhang,

Chen,

et al. 2024

Qual. Theory Dyn. Syst.

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In this paper, we focus on the existence of positive solutions for a singular Hessian equation with a negative augmented term. By finding more appropriate upper and lower solutions, we not only overcome the difficulty due to the negative augmented term but also remove a critical condition required in the existing work and establish new results for the existence of positive solutions of the equations under study. Our results improve and complement many existing works.

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Applying fixed point techniques for obtaining a positive definite solution to nonlinear matrix equations

Tariq

Ameer

Ali

et al. 2023

MATH

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<abstract><p>In this manuscript, the concept of rational-type multivalued $ F- $contraction mappings is investigated. In addition, some nice fixed point results are obtained using this concept in the setting of $ MM- $spaces and ordered $ MM- $spaces. Our findings extend, unify, and generalize a large body of work along the same lines. Moreover, to support and strengthen our results, non-trivial and extensive examples are presented. Ultimately, the theoretical results are involved in obtaining a positive, definite solution to nonlinear matrix equations as an application.</p></abstract>

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Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators

Cited by 4 publications

References 22 publications

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

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

Existence of Positive Solutions for a Singular Hessian Equation with a Negative Augmented Term

Applying fixed point techniques for obtaining a positive definite solution to nonlinear matrix equations

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