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It is well known that the roles and consequences of symmetry in mathematics and related sciences are very important. In this reprint, we aim to establish some theoretical results (and their applications) in the fields of mathematical and functional analyses, in which the concept of symmetry plays an essential role. In particular, we aim to investigate various problems in areas such as optimization problems, polynomial approximation on unbounded subsets, moment problems, variational inequalities, evolutionary problems, dynamical systems, generalized convexity, partial differential equations, and special spaces of self-adjoint operators. Some of these areas of research are strongly intercorrelated.