Let C([a,b]) be a normed space with = sup|f(x), f=C([a,b]). xe abj Consider the integral operator:...

 

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Let C([a,b]) be a normed space with = sup|f(x), f=C([a,b]). xe abj Consider the integral operator: T:C([a,b])→C([a,b]) defined by (Tf)(x) = K(x, y)ƒ (y)dy where K(,): [a,b]x[a,b]→R is a continuous function of two variables. T is bounded linear operator. Let C([a,b]) be a normed space with = sup|f(x), f=C([a,b]). xe abj Consider the integral operator: T:C([a,b])→C([a,b]) defined by (Tf)(x) = K(x, y)ƒ (y)dy where K(,): [a,b]x[a,b]→R is a continuous function of two variables. T is bounded linear operator.