Orador Convidado:

Prof. Alberto Simões, Departamento de Matemática e Centro de Matemática e Aplicações da Universidade da Beira Interior (CMA-UBI).

Resumo:

An interesting and famous talk presented by S. M. Ulam in 1940 triggered the study of stability problems for various functional equations. Ulam discussed a number of important unsolved mathematical problems. Among them, a question concerning the stability of homomorphisms seemed too abstract for anyone to reach any conclusion. In the following year, D. H. Hyers was able to give a partial solution to Ulam’s question that was the first significant breakthrough and step toward more solutions in this area. After that preliminary answer, other approaches emerged, and new orientations were introduced by Th. M. Rassias, introducing therefore the so-called Hyers-Ulam-Rassias stability. Different generalizations were obtained by other researchers, by considering the possibility of using different involved norms and others types of equations. In this talk our main goal is to present the various approaches and techniques used to study Hyers-Ulam, Hyers-Ulam-Rassias and σ-semi-Hyers-Ulam stabilities for different types of equations.

Resumo (pdf):

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