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arXiv · 2412.20764

Resolvent and Gronwall inequalities and fixed points of evolution operators

Alexander Kalinin
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Abstract

We introduce kernels and resolvents on preordered sets and derive sharp resolvent inequalities that entail Gronwall inequalities for functions of several variables. In this way, we can prove a fixed point result for operators on topological spaces that extends Banach's fixed point theorem and allows for a wide range of applications.

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Alexander Kalinin. 2024-12-30. Resolvent and Gronwall inequalities and fixed points of evolution operators. https://arxiv.org/abs/2412.20764

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