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Abstract and Applied Analysis
Volume 2013, Article ID 607204, 20 pages
http://dx.doi.org/10.1155/2013/607204
Research Article

Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces and

1İnönü Üniversitesi, Eğitim Fakültesi, A-Blok, Posta Kodu: 44280, Malatya, Turkey
2Baku State University, Department of Mech. & Math., Z. Khalilov Street, 23, P.O. Box 370145, Baku, Azerbaijan

Received 14 November 2012; Accepted 16 January 2013

Academic Editor: Juan Carlos Cortés López

Copyright © 2013 İsmet Özdemir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The spaces and 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 and by taking an arbitrary Banach space instead of , 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 and . Besides, the bounded linear integral operators on the spaces and , some of which are singular, are derived, and the solutions of the linear Fredholm integral equations of the form and are investigated in these spaces by analytical methods.