This paper, the title of which does not give a precise view of the problems discussed, treats the idea of compactness of a particular type of integral operator in the space of continuous functions. On the basis of the Arzéla-Ascoli theorem the following integral operators are discussed: \[ k\phi (x)=v(x)=\int^{x}_{0}(x/y)^{\alpha}\cdot (1- x)/(1-y)^{\beta}\cdot a(x,y)/(x\quad -y)^{\gamma}\cdot \phi (y)dy, \] where \(0\leq x\leq 1\), a(x,y)\(\subset C((0,1)\times (0,1))\), \(0\leq \alpha,\beta,\gamma <1\), for which it is shown that the functions v(x)\(\in W\subset C(0,1)\) are uniformly restricted and equal-order continuous.