Solvability for two dimensional functional integral equations via Petryshyn's fixed point theorem

This paper aims to use the Petryshyn's fixed point theorem associated with the measure of non-compactness to prove the existence of solutions of two-dimensional functional integral equations in the Banach algebra of continuous functions on the interval C([0, a] x [0, (a) over cap], R), a, (a) over cap > 0. Our existence results contains many functional integral equations as special case that arise in nonlinear analysis. Finally, we present some examples which show that our result is useful for various class of equations.

Automated summary

This paper uses the Petryshyn's fixed point theorem associated with the measure of non-compactness to prove the existence of solutions of two-dimensional functional integral equations in the Banach algebra of continuous functions on the interval C([0, a] x [0, (a) over cap], R), where a, (a) over cap > 0. The results obtained encompass various functional integral equations that arise in nonlinear analysis, and examples are provided to demonstrate the usefulness of the results for a wide range of equations.