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

Author

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  • İsmet Özdemir
  • Ali M. Akhmedov
  • Ö. Faruk Temizer

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.

Suggested Citation

  • İsmet Özdemir & Ali M. Akhmedov & Ö. Faruk Temizer, 2013. "Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces and," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-20, March.
    • Handle: RePEc:hin:jnlaaa:607204
    DOI: 10.1155/2013/607204
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