A nonstandard approach to Karamata uniform convergence theorem
\v{Z}arko Mijajlovi\'c, Danijela Brankovi\'c
TL;DR
This paper presents a nonstandard proof of a generalized Karamata uniform convergence theorem for slowly varying functions, exploring properties of a related operator and its connection to these functions.
Contribution
It introduces a novel nonstandard proof technique for the generalized theorem and analyzes properties of a related operator in this context.
Findings
Established a nonstandard proof of the generalized Karamata theorem
Analyzed properties of the operator $\\mathcal{L}$ and its relation to slowly varying functions
Extended the understanding of uniform convergence in the context of slowly varying functions
Abstract
A nonstandard proof of a generalization of Karamata uniform convergence theorem for slowly varying functions is presented. Properties of a related operator and its connection with slowly varying functions are discussed.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Stability and Controllability of Differential Equations