- Title
- A Relation-Theoretic Set-Valued Version of Presic-Ciric Theorem and Applications
- Creator
- Shukla, Satish
- Creator
- Rai, Shweta
- Creator
- Shukla, Rahul
- Subject
- Binary relation
- Subject
- Presic-Ciric operator
- Subject
- Fixed point
- Subject
- Differential inclusion
- Subject
- Difference inclusion
- Date Issued
- 2023
- Date
- 2023
- Type
- Article
- Identifier
- http://hdl.handle.net/11260/14386
- Identifier
- vital:79308
- Identifier
- 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.
- Language
- English
- Relation
- Boundary Value Problems
- Relation
- Boundary Value Problems vol 59 issue 1 21 2023 https://doi.org/10.1186/s13661-023-01748-9
- Rights
- ©2023, authors
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