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)
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 equa...
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2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/607204 |
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| author | İsmet Özdemir Ali M. Akhmedov Ö. Faruk Temizer |
| author_facet | İsmet Özdemir Ali M. Akhmedov Ö. Faruk Temizer |
| author_sort | İsmet Özdemir |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b95251061c9144388104bca2e268ff4f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b95251061c9144388104bca2e268ff4f2025-02-03T07:24:39ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/607204607204Some 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)İsmet Özdemir0Ali M. Akhmedov1Ö. Faruk Temizer2İnönü Üniversitesi, Eğitim Fakültesi, A-Blok, Posta Kodu: 44280, Malatya, TurkeyBaku State University, Department of Mech. & Math., Z. Khalilov Street, 23, P.O. Box 370145, Baku, Azerbaijanİnönü Üniversitesi, Eğitim Fakültesi, A-Blok, Posta Kodu: 44280, Malatya, TurkeyThe 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.http://dx.doi.org/10.1155/2013/607204 |
| spellingShingle | İsmet Özdemir Ali M. Akhmedov Ö. Faruk Temizer 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 |
| title | 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) |
| title_full | 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) |
| title_fullStr | 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) |
| title_full_unstemmed | 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) |
| title_short | 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) |
| title_sort | 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 |
| url | http://dx.doi.org/10.1155/2013/607204 |
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