On the integral equation $$u(x) = F(x) + \smallint G(x,\xi )u_ + ^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} (\xi ){{d\xi } \mathord{\left/ {\vphantom {{d\xi } \smallint }} \right. \kern-\nulldelimiterspace} \smallint }u_ + ^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} (\xi )d\xi $$