Abstract
In this chapter, we are interested in a certain class of integral equations, namely
the quadratic integral equation. In this case, the unknown function is treated by some
operators, then a pointwise multiplication of such operators is applied. The study of such
a kind of problem was begun in the early 60’s due to the mathematical modeling of
radiative transfer. The main objective was to present a special method or technique and
results concerning various existence for a certain quadratic integral equation.
Keywords: Quadratic integral equation, Carathéodory Theorem, Continuous solution, Iterative scheme, Maximal and minimal solutions, Comparison Theorem, δ -Approximate solutions, Hybrid functional φ-differential equation, Pantograph functional φ - differential equation.
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