Approximations by rational functions with positive coefficients

Meromorphic functions with positive coefficients

for some α (0≤α< 1). We say that f(z) is in the class ∑C(α) of such functions. The class ∑∗(α) and various other subclasses of ∑ have been studied rather extensively by Nehari and Netanyahu [9], Clunie [4], Pommerenke [11, 12], Miller [7], Royster [13], and others (cf., e.g., Bajpai [2], Goel and Sohi [6], Mogra et al. [8], Uralegaddi and Ganigi [15], Cho et al. [3], Aouf [1], and Uralegaddi an...

On the Taylor Coefficients of Rational Functions

Initial coefficients of starlike functions with real coefficients

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions

Orthogonal Rational Functions with real coefficients and semiseparable matrices

When one wants to use Orthogonal Rational Functions (ORFs) in system identification or control theory, it is important to be able to avoid complex calculations. In this paper we study ORFs whose numerator and denominator polynomial have real coefficients. These ORFs with real coefficients (RORFs) appear when the poles and the interpolation points appear in complex conjugate pairs, which is a na...

Triangular approximations of fuzzy number with value and ambiguity functions