Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces Hα,δ,γ((a,b)×(a,b),X) and Hα,δ((a,b),X)
Joint Authors
Akhmedov, Ali M.
Özdemir, İsmet
Temizer, Ö. Faruk
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-26
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
The spaces Hα,δ,γ((a,b)×(a,b),ℝ) and Hα,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 sets Hα,δ,γ((a,b)×(a,b),X) and Hα,δ((a,b),X) by taking an arbitrary Banach space X instead of ℝ, 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,γ and ∥·∥α,δ.
Besides, the bounded linear integral operators on the spaces Hα,δ,γ((a,b)×(a,b),X) and Hα,δ((a,b),X), some of which are singular, are derived, and the solutions of the linear Fredholm integral equations of the form f(s)=ϕ(s)+λ∫abA(s,t)f(t)dt,f(s)=ϕ(s)+λ∫abA(t,s)f(t)dt and f(s,t)=ϕ(s,t)+λ∫abA(s,t)f(t,s)dt are investigated in these spaces by analytical methods.
American Psychological Association (APA)
Özdemir, İsmet& Akhmedov, Ali M.& Temizer, Ö. Faruk. 2013. Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces Hα,δ,γ((a,b)×(a,b),X) and Hα,δ((a,b),X). Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-20.
https://search.emarefa.net/detail/BIM-484635
Modern Language Association (MLA)
Özdemir, İsmet…[et al.]. Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces Hα,δ,γ((a,b)×(a,b),X) and Hα,δ((a,b),X). Abstract and Applied Analysis No. 2013 (2013), pp.1-20.
https://search.emarefa.net/detail/BIM-484635
American Medical Association (AMA)
Özdemir, İsmet& Akhmedov, Ali M.& Temizer, Ö. Faruk. Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces Hα,δ,γ((a,b)×(a,b),X) and Hα,δ((a,b),X). Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-20.
https://search.emarefa.net/detail/BIM-484635
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484635