A Relation-Theoretic Set-Valued Version of Presic-Ciric Theorem and Applications
- Shukla, Satish, Rai, Shweta, Shukla, Rahul
- Authors: Shukla, Satish , Rai, Shweta , Shukla, Rahul
- Date: 2023
- Subjects: Binary relation , Presic-Ciric operator , Fixed point , Differential inclusion , Difference inclusion
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14386 , vital:79308 , DOI: https://doi.org/10.1186/s13661-023-01748-9
- Description: In this paper, we establish a relation-theoretic set-valued version of the fixed pointresult of ́Ciri ́c and Preši ́c (Acta Math. Univ. Comen. LXXVI(2):143–147,2007)onmetricspaces endowed with an arbitrary binary relation. The results of this paper, generalizeand unify the fixed point results of ́Ciri ́c and Preši ́c (Acta Math. Univ. Comen.LXXVI(2):143–147,2007), Shukla and López (Quaest. Math. 45(3):1–16,2019), andShukla and Radenovi ́c(An. ̧Stiin ̧t.Univ.‘Al.I.Cuza’Ia ̧si, Mat. 63(2):339–350,2017)inproduct spaces. Some examples are provided that justify and establish theimportance of our results. As applications of our main result, we have established theexistence of solutions to differential inclusion problems and the weak asymptoticalstability and a global attractivity of the equilibrium point of a difference inclusionproblem. The use of arbitrary binary relations in our results permits us to apply theresults to the differential inclusion problems and difference inclusion problems withweaker assumptions than those used in the papers mentioned above.
- Full Text:
- Date Issued: 2023
- Authors: Shukla, Satish , Rai, Shweta , Shukla, Rahul
- Date: 2023
- Subjects: Binary relation , Presic-Ciric operator , Fixed point , Differential inclusion , Difference inclusion
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14386 , vital:79308 , DOI: https://doi.org/10.1186/s13661-023-01748-9
- Description: In this paper, we establish a relation-theoretic set-valued version of the fixed pointresult of ́Ciri ́c and Preši ́c (Acta Math. Univ. Comen. LXXVI(2):143–147,2007)onmetricspaces endowed with an arbitrary binary relation. The results of this paper, generalizeand unify the fixed point results of ́Ciri ́c and Preši ́c (Acta Math. Univ. Comen.LXXVI(2):143–147,2007), Shukla and López (Quaest. Math. 45(3):1–16,2019), andShukla and Radenovi ́c(An. ̧Stiin ̧t.Univ.‘Al.I.Cuza’Ia ̧si, Mat. 63(2):339–350,2017)inproduct spaces. Some examples are provided that justify and establish theimportance of our results. As applications of our main result, we have established theexistence of solutions to differential inclusion problems and the weak asymptoticalstability and a global attractivity of the equilibrium point of a difference inclusionproblem. The use of arbitrary binary relations in our results permits us to apply theresults to the differential inclusion problems and difference inclusion problems withweaker assumptions than those used in the papers mentioned above.
- Full Text:
- Date Issued: 2023
Coincidence Point of Edelstein Type Mappings in Fuzzy Metric Spaces and Applications to the Stability of Dynamic Markets
- Shukla, Satish, Dubey, Nikita, Shukla, Rahul, Meznik, Ivan
- Authors: Shukla, Satish , Dubey, Nikita , Shukla, Rahul , Meznik, Ivan
- Date: 2023
- Subjects: Edelstein mapping , Fuzzy metric space , Coincidence point , Dynamic market , Demand and supply functions , Sensitivity index , Equilibrium point
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14398 , vital:79310 , DOI: https://doi.org/10.3390/axioms12090854
- Description: In this paper, we prove a coincidence point result for a pair of mappings satisfying Edelstein type contractive condition on fuzzy metric spaces. We describe the equilibrium of a simple demand– supply model of a dynamic market by the coincidence point of demand and supply functions. With the help of the coincidence point theorem in fuzzy metric spaces, it is showed that a dynamic market of a supply-sensitive nature (or demand-sensitive nature) always tends towards its equilibrium.
- Full Text:
- Date Issued: 2023
- Authors: Shukla, Satish , Dubey, Nikita , Shukla, Rahul , Meznik, Ivan
- Date: 2023
- Subjects: Edelstein mapping , Fuzzy metric space , Coincidence point , Dynamic market , Demand and supply functions , Sensitivity index , Equilibrium point
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14398 , vital:79310 , DOI: https://doi.org/10.3390/axioms12090854
- Description: In this paper, we prove a coincidence point result for a pair of mappings satisfying Edelstein type contractive condition on fuzzy metric spaces. We describe the equilibrium of a simple demand– supply model of a dynamic market by the coincidence point of demand and supply functions. With the help of the coincidence point theorem in fuzzy metric spaces, it is showed that a dynamic market of a supply-sensitive nature (or demand-sensitive nature) always tends towards its equilibrium.
- Full Text:
- Date Issued: 2023
Fixed Point Theorems in Graphical Cone Metric Spaces and Application to a System of Initial Value Problems
- Shukla, Satish, Dubey, Nikita, Shukla, Rahul
- Authors: Shukla, Satish , Dubey, Nikita , Shukla, Rahul
- Date: 2023
- Subjects: Fixed point , Graphical cone metric , Banach algebra , Contractions , System of initial value problems
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14392 , vital:79306 , DOI: https://doi.org/10.1186/s13660-023-03002-3
- Description: In this paper, we introduce the notion of graphical cone metric spaces over Banachalgebra and prove some fixed point results for a particular type of contractivemappings defined on such spaces. These results extend and generalize several resultsfrom metric, graphical metric, and cone metric spaces. Some examples thatdemonstrate the results proved herein are provided. An application of our results tothe existence of solution of a pair of initial value problems is provided.
- Full Text:
- Date Issued: 2023
- Authors: Shukla, Satish , Dubey, Nikita , Shukla, Rahul
- Date: 2023
- Subjects: Fixed point , Graphical cone metric , Banach algebra , Contractions , System of initial value problems
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14392 , vital:79306 , DOI: https://doi.org/10.1186/s13660-023-03002-3
- Description: In this paper, we introduce the notion of graphical cone metric spaces over Banachalgebra and prove some fixed point results for a particular type of contractivemappings defined on such spaces. These results extend and generalize several resultsfrom metric, graphical metric, and cone metric spaces. Some examples thatdemonstrate the results proved herein are provided. An application of our results tothe existence of solution of a pair of initial value problems is provided.
- Full Text:
- Date Issued: 2023
Some Fixed Point Theorems for a-Admissible Mappings in Complex-Valued Fuzzy Metric Spaces
- Shukla, Satish, Rai, Shweta, Shukla, Rahul
- Authors: Shukla, Satish , Rai, Shweta , Shukla, Rahul
- Date: 2023
- Subjects: Complex-valued fuzzy metric space , Admissible mapping , Fixed point , a-(y,f)-contraction
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14379 , vital:79312 , DOI: https://doi.org/10.3390/sym15091797
- Description: This paper discusses some properties of complex-valued fuzzy metric spaces and intro-duces thea-admissible mappings in the setting of complex-valued fuzzy metric spaces. We establishfixed point theorems for mappings satisfying symmetric contractive conditions with control functions.The results of this paper generalize, extend, and improve several results from metric, fuzzy metric,and complex-valued fuzzy metric spaces. Several examples are presented that verify and illustratethe new concepts, claims, and results.
- Full Text:
- Date Issued: 2023
- Authors: Shukla, Satish , Rai, Shweta , Shukla, Rahul
- Date: 2023
- Subjects: Complex-valued fuzzy metric space , Admissible mapping , Fixed point , a-(y,f)-contraction
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/11260/14379 , vital:79312 , DOI: https://doi.org/10.3390/sym15091797
- Description: This paper discusses some properties of complex-valued fuzzy metric spaces and intro-duces thea-admissible mappings in the setting of complex-valued fuzzy metric spaces. We establishfixed point theorems for mappings satisfying symmetric contractive conditions with control functions.The results of this paper generalize, extend, and improve several results from metric, fuzzy metric,and complex-valued fuzzy metric spaces. Several examples are presented that verify and illustratethe new concepts, claims, and results.
- Full Text:
- Date Issued: 2023
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