No abstract

We generalize the construction of the ordinary Sierpiński triangle to obtain a two-parameter family of fractals we call Sierpiński pedal triangles. These fractals are obtained from a given triangle by recursively deleting the associated pedal triangles in a manner analogous to the construction of the ordinary Sierpiński triangle, but their fractal dimensions depend on the choice of the initial triangles. In this paper, we discuss the fractal dimensions of the Sierpiński pedal triangles and the related area ratio problem, and provide some computer-generated graphs of the fractals. Fractals 2008.16:141-150. Downloaded from www.worldscientific.com by MCGILL UNIVERSITY on 02/03/15. For personal use only. Fractals 2008.16:141-150. Downloaded from www.worldscientific.com by MCGILL UNIVERSITY on 02/03/15. For personal use only.

In this paper we construct sequences of polygons from a given nsided cyclic polygon by iterated procedures and study the limiting behaviors of these sequences in terms of nonnegative matrices and Markov chains.

Abstract. In this paper, we show that Schur-convex functions share some important properties with the ordinary convex functions. We apply special properties of Schur-convex functions to establish some inequalities for the generalized power means that include many well-known classical analytic inequalities as special cases.Mathematics subject classification (1991): 26B25, 26D05, 26D10.