scholarly journals Solvability of a Quadratic Integral Equation of Fredholm Type Via a Modified Argument

2020 ◽  
Author(s):  
İlyas Dal ◽  
Ömer Faruk Temizer
Keyword(s):  
Integral Equation ◽  
Fredholm Type ◽  
Quadratic Integral Equation ◽  
Quadratic Integral

scholarly journals On the Existence of the Solutions of a Fredholm Integral Equation with a Modified Argument in Hölder Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 522 ◽  
Author(s):  
Merve Temizer Ersoy ◽  
Hasan Furkan
Keyword(s):  
Integral Equation ◽  
Existence Of Solutions ◽  
Hölder Spaces ◽  
Fredholm Type ◽  
Relative Compactness ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Conclusion Section ◽  
The Given ◽  
Holder Spaces

This article concerns the entity of solutions of a quadratic integral equation of the Fredholm type with an altered argument, x ( t ) = p ( t ) + x ( t ) ∫ 0 1 k ( t , τ ) ( T x ) ( τ ) d τ , where p , k are given functions, T is the given operator satisfying conditions specified later and x is an unknown function. Through the classical Schauder fixed point theorem and a new conclusion about the relative compactness in Hölder spaces, we obtain the existence of solutions under certain assumptions. Our work is more general than the previous works in the Conclusion section. At the end, we introduce several tangible examples where our entity result can be adopted.

scholarly journals Solvability of a Quadratic Integral Equation of Fredholm Type with Supremum in Hölder Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
J. Caballero Mena ◽  
R. Nalepa ◽  
K. Sadarangani
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Hölder Condition ◽  
Fredholm Type ◽  
Quadratic Integral Equation ◽  
Quadratic Integral ◽  
Holder Spaces

Using the classical Schauder fixed point theorem, we prove the existence of solutions of a quadratic integral equation of Fredholm type with supremum in the space of functions satisfying the Hölder condition.

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