Jan Szynal

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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)
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)
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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