We study the norm derivatives in context of Birkhoff–James orthogonality real Banach spaces. As an application this, we obtain a complete characterization left-symmetric points and right-symmetric space terms derivatives. strong $$\ell _1^n$$ _\infty ^n$$ also relation defined by some newly introduced variation orthogonality. further orthogonality, approximate smoothness attainment bounded bili...

Two different notions of approximate Birkhoff–James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieliński. In the present paper we consider a global local symmetry related to each two definitions. We prove that considered is approximately symmetric sense all finite-dimensional Banach spaces. For other case, for polyhedral spaces, equivalent some newly geometric ...

We study best approximations in Banach spaces via Birkhoff–James orthogonality of functionals. To exhibit the usefulness techniques approximation problems, some algorithms and distance formulae are presented. As an application our study, we obtain crucial inequalities, which also strengthen classical Hölder’s inequality. The relevance inequalities discussed through concrete examples.