[tex]\varphi(x)=f(x)+\int^{b}_{a}K(x,y)\varphi(y)dt[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]f:[a.b]→ℝ[/tex]

[tex]K(x,y)→[a,b]\times [a,b]→ℝ[/tex]

Is [tex][a,b]\times [a,b][/tex] Deckart product? Is that the way to construct [tex]ℝ^2[/tex] space?

If I say [tex]f\in C([a,b])[/tex], [tex]K\in C([a,b]\times [a,b])[/tex] that means that [tex]f[/tex] and [tex]K[/tex] are differentiable on this intervals. Right?

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# Defining of function in equation

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