Linear Integral Operators (K. Jörgens)

SIAM Review ◽  
1984 ◽  
Vol 26 (1) ◽  
pp. 128-129
Author(s):  
James A. Cochran
Keyword(s):  
Integral Operators ◽  
Linear Integral ◽  
Linear Integral Operators

Non-linear integral operators

1976 ◽  
pp. 349-449
Author(s):  
M. A. Krasnoselskii ◽  
P. P. Zabreiko ◽  
E. I. Pustylnik ◽  
P. E. Sbolevskii
Keyword(s):  
Integral Operators ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Integral Operators

Continuity and compactness of linear integral operators

1976 ◽  
pp. 64-172
Author(s):  
M. A. Krasnoselskii ◽  
P. P. Zabreiko ◽  
E. I. Pustylnik ◽  
P. E. Sbolevskii
Keyword(s):  
Integral Operators ◽  
Linear Integral ◽  
Linear Integral Operators

scholarly journals Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the SpacesHα,δ,γ((a,b)×(a,b),X)andHα,δ((a,b),X)

2013 ◽  
Vol 2013 ◽  
pp. 1-20
Author(s):  
İsmet Özdemir ◽  
Ali M. Akhmedov ◽  
Ö. Faruk Temizer
Keyword(s):  
Banach Space ◽  
Numerical Methods ◽  
Banach Spaces ◽  
Integral Equations ◽  
Singular Integral ◽  
Integral Operators ◽  
Fredholm Integral Equations ◽  
Bounded Linear ◽  
Linear Integral ◽  
Linear Integral Operators

The spacesHα,δ,γ((a,b)×(a,b),ℝ)andHα,δ((a,b),ℝ)were defined in ((Hüseynov (1981)), pages 271–277). Some singular integral operators on Banach spaces were examined, (Dostanic (2012)), (Dunford (1988), pages 2419–2426 and (Plamenevskiy (1965)). The solutions of some singular Fredholm integral equations were given in (Babolian (2011), Okayama (2010), and Thomas (1981)) by numerical methods. In this paper, we define the setsHα,δ,γ((a,b)×(a,b),X)andHα,δ((a,b),X)by taking an arbitrary Banach spaceXinstead ofℝ, and we show that these sets which are different from the spaces given in (Dunford (1988)) and (Plamenevskiy (1965)) are Banach spaces with the norms∥·∥α,δ,γand∥·∥α,δ. Besides, the bounded linear integral operators on the spacesHα,δ,γ((a,b)×(a,b),X)andHα,δ((a,b),X), some of which are singular, are derived, and the solutions of the linear Fredholm integral equations of the formf(s)=ϕ(s)+λ∫abA(s,t)f(t)dt,f(s)=ϕ(s)+λ∫abA(t,s)f(t)dtandf(s,t)=ϕ(s,t)+λ∫abA(s,t)f(t,s)dtare investigated in these spaces by analytical methods.

scholarly journals Nontrivial Solutions for a System of Fractional q-Difference Equations Involving q-Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 828 ◽  
Author(s):  
Yaohong Li ◽  
Jie Liu ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Integral Boundary Conditions ◽  
Integral Operators ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Integral Boundary ◽  
The First Eigenvalue ◽  
Linear Integral ◽  
Linear Integral Operators

In this paper, we study the existence of nontrivial solutions for a system of fractional q-difference equations involving q-integral boundary conditions, and we use the topological degree to establish our main results by considering the first eigenvalue of some associated linear integral operators.

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