Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations

Younis, Mudasir; Ahmad, Haroon; Chen, Lili; Han, Maoan

doi:10.1016/j.geomphys.2023.104955

Cited by 25 publications

(9 citation statements)

References 21 publications

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“…Typical applications of this kind include the flow of information in communication networks in which graphs model data transfer, bandwidth capacities, signal strengths, communication costs, latency, etc. [18][19][20]. Similarly, dependency relationships in project management represent priorities in tasks that need to be completed before other tasks can begin; while in social networks, the frequency of interactions between people on social media platforms, etc., is typically modelled.…”

Section: Semi-local Integration Measure For Directed and Weighted Graphsmentioning

confidence: 99%

Semi-Local Integration Measure for Directed Graphs

Ban Kirigin,

Bujačić Babić

2024

Mathematics

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Directed and weighted graphs can be used for many real-world applications to model and analyse the quality and structure of communication within the system, the distribution and flow of information, and various resources, dependencies, resilience, etc. On social media platforms, for example, highly networked members, so-called influencers, disseminate information, opinions and trends to their followers, who in turn increase the popularity of the influencers through likes and comments. Both types of interaction have a major influence on discussions and activities in the social network. To identify the nodes with the highest integration and interconnectivity within the neighbourhood subnetwork, we introduce the Directed Semi-Local Integration (DSLI) centrality measure for directed and weighted graphs. This centrality measure evaluates the integration of nodes assessed by the presence of connection, the strength of links, the organisation and optimisation of inbound and outbound interconnectivity, and the redundancy in the local subnetwork, and provides a stronger differentiation of the importance of nodes than standard centrality measures. Thus, DSLI has the potential to be used for analysing the degree of integration for the uptake and dissemination of resources in complex networks in many different contexts.

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Section: Semi-local Integration Measure For Directed and Weighted Graphsmentioning

confidence: 99%

Semi-Local Integration Measure for Directed Graphs

Ban Kirigin,

Bujačić Babić

2024

Mathematics

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“…This method provides a novel framework for solving nonlinear problems that arise in the real world and has many applications in engineering and technology. In [ 10 ] they investigates fixed point convergence in graphical B c –Kannan–contractions within graphical extended b –metric spaces. In [ 11 ] using an alternating distance function, they report new findings on coincidence, best proximity, and fixed points in multivalued proximal contractions within b -metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy fixed point approach to study the existence of solution for Volterra type integral equations using fuzzy Sehgal contraction

Zahid,

Ud Din,

Shah

et al. 2024

PLoS ONE

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In this manuscript, we present a novel concept known as the fuzzy Sehgal contraction, specifically designed for self-mappings defined in the context of a fuzzy metric space. Our primary objective is to explore the existence and uniqueness of fixed points for self-mappings in fuzzy metric space. To support our conclusions, we present a detailed illustrative case that demonstrates the superiority of the convergence obtained with our suggested method to those currently recorded in the literature. Moreover, we provide graphical depictions of the convergence behavior, which makes our study more understandable and transparent. Additionally, we extend the application of our results to address the existence and uniqueness of solutions for Volterra integral equations.

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“…Numerous disciplines of pure and applied mathematics, including nonlinear functional analysis, and the numerical solutions of differential equations make substantial use of fixed point theory ( [1]). Banach contraction principle (BCP), which is a key finding in metric fixed point theory provides a useful method for solving functional equations.…”

Section: Introductionmentioning

confidence: 99%

Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces

Ali,

Nazir

et al. 2023

Mathematics

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In order to generalize classical Banach contraction principle in the setup of quasi-metric spaces, we introduce Suzuki-type contractions of quasi-metric spaces and prove some fixed point results. Further, we suggest a correction in the definition of another class of quasi-metrics known as Δ-symmetric quasi-metrics satisfying a weighted symmetry property. We discuss equivalence of various types of completeness of Δ-symmetric quasi-metric spaces. At the end, we consider the existence of fixed points of generalized Suzuki-type contractions of Δ-symmetric quasi-metric spaces. Some examples have been furnished to make sure that generalizations we obtain are the proper ones.

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Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations

Cited by 25 publications

References 21 publications

Semi-Local Integration Measure for Directed Graphs

Semi-Local Integration Measure for Directed Graphs

Fuzzy fixed point approach to study the existence of solution for Volterra type integral equations using fuzzy Sehgal contraction

Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces

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