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Results presented in this chapter are related to the mutual relationship between generalized inverse relations, weak asymptotic equivalence relations, and strong asymptotic equivalence relations in certain classes of functions studied in Karamata’s theory of regular variability. Starting from notions of regular variability, generalized inverse, weak and strong equivalence relations, and Theorem A, which was proved in one of its forms in the paper Balkema et al. (Q J Math Oxford Ser 30(2):385–416, 1979), we will present theorems which represent the characteristics of certain functional classes.

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Karamata’s Theory, Asymptotic Relations, and the Generalized Inverse

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  • 发表日期：

    2025年

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  • Rale M. Nikolić,
  • Valentina Timotić,
  • Dragan Djurčić

摘要

Results presented in this chapter are related to the mutual relationship between generalized inverse relations, weak asymptotic equivalence relations, and strong asymptotic equivalence relations in certain classes of functions studied in Karamata’s theory of regular variability. Starting from notions of regular variability, generalized inverse, weak and strong equivalence relations, and Theorem A, which was proved in one of its forms in the paper Balkema et al. (Q J Math Oxford Ser 30(2):385–416, 1979), we will present theorems which represent the characteristics of certain functional classes.