ON THE INTEGRAL EQUATION tex2html_wrap_inline14 WHERE tex2html_wrap_inline16 , tex2html_wrap_inline18 .

JYRKI PIILA AND JUHANI PITKÄRANTA

Abstract:

In the present paper we consider a function f which is a solution of the integral equation

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Here g is a given, smooth function defined on the interval [0,1], tex2html_wrap_inline28 is a constant, and L is a continuous piecewise linear function through the points (0,0), tex2html_wrap_inline34 , (1,1), where also a>1 is a constant. We mainly focus our attention on the regularity properties of f. Away from the origin the regularity is analyzed by applying the Banach fixed point theorem, while near the origin we get a singular expansion for f by using the Mellin transform techniques.