Fixed Point Results via Real-Valued Function Satisfying Intergral Type Rational Contraction
- Mani, Naveen, Sharma, Amit, Shukla, Rahul
- Authors: Mani, Naveen , Sharma, Amit , Shukla, Rahul
- Date: 2023
- Subjects: Real-Valued function , Fixed Point , Satisfying Integral Type Contractions
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14269 , vital:79174 , DOI: https://doi.org/10.1155/2023/2592507
- Description: In this article, we mainly discuss the existence and uniqueness offixed point satisfying integral type contractions in completemetric spaces via rational expression using real-valued functions. We improve and unify many widely known results from theliterature. Among these, the work of Rakotch (1962), Branciari (2002), and Liu et al. (2013) is extended. Finally, we concludewith an example presented graphically in favour of our work.
- Full Text:
- Date Issued: 2023
- Authors: Mani, Naveen , Sharma, Amit , Shukla, Rahul
- Date: 2023
- Subjects: Real-Valued function , Fixed Point , Satisfying Integral Type Contractions
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14269 , vital:79174 , DOI: https://doi.org/10.1155/2023/2592507
- Description: In this article, we mainly discuss the existence and uniqueness offixed point satisfying integral type contractions in completemetric spaces via rational expression using real-valued functions. We improve and unify many widely known results from theliterature. Among these, the work of Rakotch (1962), Branciari (2002), and Liu et al. (2013) is extended. Finally, we concludewith an example presented graphically in favour of our work.
- Full Text:
- Date Issued: 2023
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.
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- Date Issued: 2023
- 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.
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- Date Issued: 2023
Mann-Dotson's Algorithm for a Countable Family of Non-Self Strict Pseudo-Contractive Mappings
- Patel, Prashant, Shukla, Rahul
- Authors: Patel, Prashant , Shukla, Rahul
- Date: 2023
- Subjects: Pseudocontractive mapping , Inward condition , Banach space
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14249 , vital:79173 , DOI: https://doi.org/10.1007/s12215-023-00912-5
- Description: The aim of this paper to present some weak and strong convergence results for countablefamily of non-self mappings. More precisely, we employ the Mann–Dotson’s algorithm toapproximatecommonfixedpointsofacountablefamilyofnon-selfk-strictPseudocontractivemappings inq-uniformly smooth Banach spaces.
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- Date Issued: 2023
- Authors: Patel, Prashant , Shukla, Rahul
- Date: 2023
- Subjects: Pseudocontractive mapping , Inward condition , Banach space
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14249 , vital:79173 , DOI: https://doi.org/10.1007/s12215-023-00912-5
- Description: The aim of this paper to present some weak and strong convergence results for countablefamily of non-self mappings. More precisely, we employ the Mann–Dotson’s algorithm toapproximatecommonfixedpointsofacountablefamilyofnon-selfk-strictPseudocontractivemappings inq-uniformly smooth Banach spaces.
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- Date Issued: 2023
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:
- Date Issued: 2023
- 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.
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- Date Issued: 2023
Some Fixed-Point Theorems of Convex Orbital(α,β)-Contractions Mappings in Geodesic
- Authors: Shukla, Rahul
- Date: 2023
- Subjects: Iterated contraction , Geodesic space , Partial order
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14257 , vital:79169 , DOI: https://doi.org/10.1186/s13663-023-00749-8
- Description: The aim of this paper is to broaden the applicability of convex orbital(α,β)-contraction mappings to geodesic spaces. This class of mappings is a naturalextension of iterated contraction mappings. The paper derives fixed-point theoremsboth with and without assuming continuity. Furthermore, the paper investigatesmonotone convex orbital (α,β)-contraction mappings and establishes a fixed-pointtheorem for this class of mappings.
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- Date Issued: 2023
- Authors: Shukla, Rahul
- Date: 2023
- Subjects: Iterated contraction , Geodesic space , Partial order
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14257 , vital:79169 , DOI: https://doi.org/10.1186/s13663-023-00749-8
- Description: The aim of this paper is to broaden the applicability of convex orbital(α,β)-contraction mappings to geodesic spaces. This class of mappings is a naturalextension of iterated contraction mappings. The paper derives fixed-point theoremsboth with and without assuming continuity. Furthermore, the paper investigatesmonotone convex orbital (α,β)-contraction mappings and establishes a fixed-pointtheorem for this class of mappings.
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- Date Issued: 2023
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