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Volume 2020

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

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Abstract: In this paper, we decompose an operator as the sum of an increasing operator and a decreasing operator, with a condition that the change in the increasing component is greater than the change in the decreasing component on a given set, which allows us to use a monotonic iterative method to find a fixed point for the operator. We illustrate the method by applying it to the second-order right focal boundary value problem, proving the existence of a positive solution.

Keywords: fixed-point theorems, monotonic, alternate inversion, iterative.

DOI: 10.30697/rfpta-2018-037

How to cite this article: Richard I. Avery, Douglas R. Anderson and Johnny Henderson, Layered Monotonic Fixed Point Theorem, Res. Fixed Point Theory Appl.,Volume 2020, Article ID 2018037, 10 pages, 2020. DOI: https://doi.org/10.30697/rfpta-2018-037

Copyright © 2019 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.