On the Existence of the Solutions of a Fredholm Integral Equation with a Modified Argument in Hölder Spaces
Keyword(s):
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.
2020 ◽
Vol 490
(1)
◽
pp. 124237
2018 ◽
Vol 8
(1)
◽
pp. 1099-1110
◽
2019 ◽
Vol 40
(10)
◽
pp. 1150-1168
◽
2006 ◽
Vol 51
(6-7)
◽
pp. 1065-1074
◽
2013 ◽
Vol 33
(1)
◽
pp. 95-109
◽
2013 ◽
Vol 21
(1)
◽
pp. 52-56
◽