We introduce order-k α-hulls and αshapes — generalizations of α-hulls and α-shapes. Being also a generalization of k-hull (known in statistics as “k-depth contour”), order-k α-hull provides a link between shape reconstruction and statistical depth. As a generalization of α-hull, order-k α-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k α-shape p...

We investigate interlacing properties of zeros Laguerre polynomials Ln(α)(x) and Ln+1(α+k)(x), α>−1, where n∈N k∈{1,2}. prove that, in general, the these interlace partially not fully. The sharp t-interval within which two equal degree Ln(α+t)(x) are for every each α>−1 is 0<t≤ 2, [Driver K, Muldoon ME. Sharp interval polynomials. J Approx Theory, to appear.], consecutive Ln−1(α+t)(x) 0≤t≤ Comm...

the goal of this paper is to generalize the recently introduced summability method and introduce double statistical convergence of order  by using ideal. we also investigate certain properties of this convergence.