Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces H-alpha,H-delta,H-gamma ((a,b) x (a,b), X) and H-alpha,H-delta(a,b), X)

ÖZDEMIR I., AKHMEDOV A. M., TEMİZER Ö. F.

ABSTRACT AND APPLIED ANALYSIS, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası:
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1155/2013/607204
  • Dergi Adı: ABSTRACT AND APPLIED ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • İnönü Üniversitesi Adresli: Evet

Özet

The spaces H-alpha,H-delta,H-gamma ((a,b) x (a,b), R) and H-alpha,H-delta ((a,b), R) were defined in ((Huseynov (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 H-alpha,H-delta,H-gamma ((a,b) x(a,b), X) and H-alpha,H-delta ((a,b), X) by taking an arbitrary Banach space X instead of R, and we showthat these sets which are different from the spaces given in (Dunford (1988)) and (Plamenevskiy (1965)) are Banach spaces with the norms parallel to center dot parallel to(alpha,delta,gamma) and parallel to . parallel to(alpha,delta) Besides, the bounded linear integral operators on the spaces H-alpha,H-delta,H-gamma ((a,b) x (a,b), X) and H-alpha,H-delta ((a,b), X), some of which are singular, are derived, and the solutions of the linear Fredholmintegral equations of the form f(s) = phi(s) + lambda integral(b)(a)A(s,t) f(t)dt, f(s) = phi(s) + lambda integral(b)(a)A(t,s)f(t)dt and f(s, t) = phi(s, t) + lambda integral(b)(a) (s, t)f(t, s)dt are investigated in these spaces by analytical methods.