Fixed Point Theory in External Parametric Sb-Metric Spaces and Its Applications
- Mani, Naveen, Beniwal, Sunil, Shukla, Rahul, Megha, Pingale
- Authors: Mani, Naveen , Beniwal, Sunil , Shukla, Rahul , Megha, Pingale
- Date: 2023
- Subjects: Metric space , Fixed point , Parametic , Linear , Contraction
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14265 , vital:79171 , DOI: https://doi.org/10.3390/sym15122136
- Description: This article introduces the novel concept of an extended parametric Sb-metric space, which is a generalization of both Sb-metric spaces and parametric Sb-metric spaces. Within this extended framework, we first establish an analog version of the Banach fixed-point theorem for self-maps.We then prove an improved version of the Banach contraction principle for symmetric extended parametric Sb-metric spaces, using an auxiliary function to establish the desired result. Finally, we provide illustrative examples and an application for determining solutions to Fredholm integralequations, demonstrating the practical implications of our work.
- Full Text:
- Authors: Mani, Naveen , Beniwal, Sunil , Shukla, Rahul , Megha, Pingale
- Date: 2023
- Subjects: Metric space , Fixed point , Parametic , Linear , Contraction
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14265 , vital:79171 , DOI: https://doi.org/10.3390/sym15122136
- Description: This article introduces the novel concept of an extended parametric Sb-metric space, which is a generalization of both Sb-metric spaces and parametric Sb-metric spaces. Within this extended framework, we first establish an analog version of the Banach fixed-point theorem for self-maps.We then prove an improved version of the Banach contraction principle for symmetric extended parametric Sb-metric spaces, using an auxiliary function to establish the desired result. Finally, we provide illustrative examples and an application for determining solutions to Fredholm integralequations, demonstrating the practical implications of our work.
- Full Text:
Some Convergence Results for a Sequence of Gornicki Type Contractions Mappings
- Panicker, Rekha, Shukla, Rahul, Vijayasenan, Deepa
- Authors: Panicker, Rekha , Shukla, Rahul , Vijayasenan, Deepa
- Date: 2023
- Subjects: Metric space , Gornicki contraction mapping , (G)-convergence , (H)-convergence
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14245 , vital:79168 , DOI: https://doi.org/10.28919/afpt/8215
- Description: The stability of fixed points for a sequence of mappings satisfying the conditions introduced by Górnicki is studied in a metric space(X;d). In particular, these mappings are only defined on a subsetXnof themetric spaceX. In this paper, we study the convergence of Tng and the convergence of its fixed points, fxng. We also illustrate our results by applying them to an initial value problem for an ordinary differential equation.
- Full Text:
- Authors: Panicker, Rekha , Shukla, Rahul , Vijayasenan, Deepa
- Date: 2023
- Subjects: Metric space , Gornicki contraction mapping , (G)-convergence , (H)-convergence
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14245 , vital:79168 , DOI: https://doi.org/10.28919/afpt/8215
- Description: The stability of fixed points for a sequence of mappings satisfying the conditions introduced by Górnicki is studied in a metric space(X;d). In particular, these mappings are only defined on a subsetXnof themetric spaceX. In this paper, we study the convergence of Tng and the convergence of its fixed points, fxng. We also illustrate our results by applying them to an initial value problem for an ordinary differential equation.
- Full Text:
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