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On 6 July, at VNUHCM–University of Science (HCMUS), doctoral researcher Nguyễn Thị Thanh Lý successfully defended her doctoral thesis in Mathematical Analysis. The thesis, entitled “Ulam-Hyers stability of some functional equations and applications”, was completed under the academic supervision of Associate Professor Nguyễn Văn Dũng and Associate Professor Lý Kim Hà.

The doctoral thesis focuses on the stability of several vital classes of functional equations in modern analysis, including generalized multilinear functional equations, generalized quadratic functional equations, generalized mixed additive–quadratic functional equations, and generalized cubic functional equations in quasi-Banach and quasi-p-Banach spaces. These research areas hold significant importance within functional equation theory and functional analysis, helping to clarify problems regarding the stability of solutions under the influence of small deviations or perturbations.

Utilizing research methodologies from modern analysis and the stability theory of functional equations, the thesis establishes sufficient conditions for the Ulam-Hyers stability of the aforementioned classes of functional equations. The achieved results not only extend the scope of application for numerous previously published works but also provide fresh approaches to studying stability within generalized spaces.

Among the prominent outcomes of this research is the formulation of corollaries for multiple special cases of functional equations, alongside answers to several open questions in the field. Furthermore, the doctoral researcher constructed counterexamples and illustrative examples to clarify the limitations of the theoretical findings and evaluate the applicability of the proposed methods.

The research findings have been published in three international scientific papers indexed in the Web of Science (WoS), comprising one Q1 journal article, one Q2 journal article, and one Q3 journal article.

In terms of scientific significance, the thesis contributes to developing the stability theory of functional equations in generalized spaces, whilst providing further theoretical tools and illustrative examples that can be inherited, extended, or applied in related research directions. The results and approaches presented in the thesis can also be further developed to investigate the stability of other classes of functional equations in quasi-Banach, quasi-p-Banach, and more generalized spaces.