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# Layered Compression-Expansion Fixed Point Theorem-by Richard I. Avery, Douglas R. Anderson and Johnny Henderson

Abstract: The layered compression-expansion fixed point theorem is an alternative approach to the Krasnoselskii fixed point theorem for perturbed operators. The layered compression-expansion fixed point theorem is used to verify the existence of a fixed point to an operator of the form $T = R+S$ (sum of operators) by verifying the existence of a fixed point for the operator defined by $M(r,s) = (R(r+s),S(r+s))$. This result is extended to the sum of $k$ operators. Moreover, an example illustrating this technique applied to a conformable right focal boundary value problem is provided.