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
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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