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- IWONA NARANIECKA, JAN SZYNAL, ANNA TATARCZAK
- 2011

Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region… (More)

- DMITRI V. PROKHOROV, JAN SZYNAL, Juha M. Heinonen
- 2003

Let K(φ) be the class of functions f(z) = z+a2z + . . . which are holomorphic and convex in direction eiφ in the unit disk D, i.e. the domain f(D) is such that the intersection of f(D) and any straight line {w : w = w0 + teiφ, t ∈ R} is a connected or empty set. In this note we determine the radius rψ,φ of the biggest disk |z| ≤ rψ,φ with the property that… (More)

- Michael Dorff, Iwona Naraniecka, Jan Szynal
- 2003

We introduce the class L(β, γ) of holomorphic, locally univalent functions in the unit disk D = {z : |z| < 1}, which we call the class of doubly close-to-convex functions. This notion unifies the earlier known extensions [4], [1], [12]. The class L(β, γ) appears to be linear invariant. First of all we determine the region of variability {w : w = log f ′(r),… (More)

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