Existence of Solutions: Investigating Fredholm Integral Equations via a Fixed-Point Theorem
Abstract
:1. Introduction
2. Preliminaries
3. Existence Theorem
- (i)
- ,
- (ii)
- The continuous function satisfies the tempered by the modulus of continuity with respect to the first variable, that is, there exists a constant such that
- (iii)
- Let be a continuous operator on with respect to norm and be a non-decreasing function, the following inequality is satisfied for each
- (iv)
- There exists a positive solution of the inequality
4. Applications
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Özger, F.; Temizer Ersoy, M.; Ödemiş Özger, Z. Existence of Solutions: Investigating Fredholm Integral Equations via a Fixed-Point Theorem. Axioms 2024, 13, 261. https://doi.org/10.3390/axioms13040261
Özger F, Temizer Ersoy M, Ödemiş Özger Z. Existence of Solutions: Investigating Fredholm Integral Equations via a Fixed-Point Theorem. Axioms. 2024; 13(4):261. https://doi.org/10.3390/axioms13040261
Chicago/Turabian StyleÖzger, Faruk, Merve Temizer Ersoy, and Zeynep Ödemiş Özger. 2024. "Existence of Solutions: Investigating Fredholm Integral Equations via a Fixed-Point Theorem" Axioms 13, no. 4: 261. https://doi.org/10.3390/axioms13040261