Existence of integrals and the solution of integral equations

Abstract

Functions are from R to N or R × R R \times R to N , where R denotes the real numbers and N denotes a normed complete ring. If S, T and G are functions from R × R R \times R to N , each of S ( p − , p ) , S ( p − , p − ) , T ( p − , p ) S({p^ - },p),S({p^ - },{p^ - }),T({p^ - },p) and T ( p − , p − ) T({p^ - },{p^ - }) exists for a > p ⩽ b a > p \leqslant b , each of S ( p , p + ) , S ( p + , p + ) , T (