The paper studies L 1 (IR d)-norm approximations from a space spanned by a discrete set of translates of a basis function. Attention here is restricted to functions whose Fourier transform is smooth on IR d n0, and has a singularity at the origin. Examples of such basis functions are the thin-plate splines and the multiquadrics, as well as other types of radial basis functions that are employed...

In this paper‎, ‎we introduce a new class$T_{k}^{s,a}[A,B,alpha‎ ,‎beta ]$ of analytic functions by using a‎ ‎newly defined convolution operator‎. ‎This class contains many known classes of‎ ‎analytic and univalent functions as special cases‎. ‎We derived some‎ ‎interesting results including inclusion relationships‎, ‎a radius problem and‎ ‎sharp coefficient bound for this class‎.

The authors propose an improved decision-based detail-preserving variational method (DPVM) for removal of random-valued impulse noise. In the denoising scheme, adaptive centre weighted median filter (ACWMF) is first ameliorated by employing the variable window technique to improve its detection ability in highly corrupted images. Based on the improved ACWMF, a fast iteration strategy is used to...