Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

Abstract We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) bounded variation. In our approach we define analogue the partial sums with help Dirichlet kernel using newly defined weighted metric integral. derive error bounds for these approximants. As a consequence, prove that sequence converges pointwisely in Hausdorff values approximated function at its points continuity, or certain set described terms selections multifunction point discontinuity. Our are obtained new notions one-sided local moduli quasi-moduli continuity which discuss more generally spaces.