Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar
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Mudasir Younis
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Deepak Singh
Abstract
The purpose of this article is to present the notion of graphical extended b-metric spaces, blending the concepts of graph theory and metric fixed point theory. We discuss the structure of an open ball of the new proposed space and elaborate on the newly introduced ideas in a novel way by portraying suitably directed graphs. We also provide some examples in graph structure to show that our results are sharp as compared to the results in the existing state-of-art. Furthermore, an application to the transverse oscillations of a homogeneous bar is entrusted to affirm the applicability of the established results. Additionally, we evoke some open problems for enthusiastic readers for the future aspects of the study.
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Author contribution: All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Coordinated target tracking in sensor networks by maximizing mutual information
- Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties
- Computational study of intravenous magnetic drug targeting using implanted magnetizable stent
- Extended logistic map for encryption of digital images
- Valuation of the American put option as a free boundary problem through a high-order difference scheme
- Power minimization of gas transmission network in fully transient state using metaheuristic methods
- A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds
- Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation
- Dynamic characteristics of supersonic turbulent free jets from four types of circular nozzles
- New insights into singularity analysis
- Chaos and bifurcations in a discretized fractional model of quasi-periodic plasma perturbations
- Wavelet collocation methods for solving neutral delay differential equations
- Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method
- Solving nonlinear third-order boundary value problems based-on boundary shape functions
- Positive radial solutions for Dirichlet problems involving the mean curvature operator in Minkowski space
- Effect of outlet impeller diameter on performance prediction of centrifugal pump under single-phase and cavitation flow conditions
- A fractional-order ship power system: chaos and its dynamical properties
- Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar
- Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations
- Modelling and numerical synchronization of chaotic system with fractional-order operator
