We study symmetric points with respect to (ϱ+)-orthogonality, (ϱ−)-orthogonality and ϱ-orthogonality in the space C(K, \(\mathbb{X}\) ), where K is a perfectly normal, compact space and \(\mathbb{X}\) is a Banach space. We characterize left symmetric points and right symmetric points in C(K, \(\mathbb{X}\) ) with respect to (ϱ+)-orthogonality and (ϱ−)-orthogonality, separately. Furthermore, we provide necessary conditions for left symmetric and right symmetric points with respect to ϱ-orthogonality. As an application of these results we also study these symmetric points in the space of operators defined on some special Banach spaces.
