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.
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
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