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

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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.

Keywords: Fixed-point theorems, cross product, alternate inversion, compression-expansion, layered, sum of operators, conformable derivative, right focal problem.

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How to cite this article: Richard I. Avery, Douglas R. Anderson and Johnny Henderson, Layered Compression-Expansion Fixed Point Theorem, Results in Fixed Point Theory and Applications, vol. 2018, Article ID 201825, 10 pages, 2018.

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Copyright © 2018 SUMA Publishing Group., This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.