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- Title
Existence of Solutions: Investigating Fredholm Integral Equations via a Fixed-Point Theorem.
- Authors
Özger, Faruk; Temizer Ersoy, Merve; Ödemiş Özger, Zeynep
- Abstract
Integral equations, which are defined as "the equation containing an unknown function under the integral sign", have many applications of real-world problems. The second type of Fredholm integral equations is generally used in radiation transfer theory, kinetic theory of gases, and neutron transfer theory. A special case of these equations, known as the quadratic Chandrasekhar integral equation, given by x (s) = 1 + λ x (s) ∫ 0 1 s t + s x (t) d t , can be very often encountered in many applications, where x is the function to be determined, λ is a parameter, and t , s ∈ [ 0 , 1 ] . In this paper, using a fixed-point theorem, the existence conditions for the solution of Fredholm integral equations of the form χ (l) = ϱ (l) + χ (l) ∫ p q k (l , z) (V χ) (z) d z are investigated in the space C ω p , q , where χ is the unknown function to be determined, V is a given operator, and ϱ , k are two given functions. Moreover, certain important applications demonstrating the applicability of the existence theorem presented in this paper are provided.
- Subjects
FREDHOLM equations; INTEGRAL equations; KINETIC theory of gases; QUADRATIC equations; EXISTENCE theorems; INTEGRAL functions
- Publication
Axioms (2075-1680), 2024, Vol 13, Issue 4, p261
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms13040261