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An Application of the Subordination Chains

Irina Oros, Georgia (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 30C45, 30A20, 34A30The notion of differential superordination was introduced in [4] by S.S. Miller and P.T. Mocanu as a dual concept of differential subordination [3] and was developed in [5]. The notion of strong differential subordination was introduced by J.A. Antonino and S. Romaguera in [1]. In [6] the author introduced the dual concept of strong differential superordination. In this paper we study strong differential superordination using the subordination chains.

An example for the holomorphic sectional curvature of the Bergman metric

Żywomir Dinew (2010)

Annales Polonici Mathematici

We study the behaviour of the holomorphic sectional curvature (or Gaussian curvature) of the Bergman metric of planar annuli. The results are then utilized to construct a domain for which the curvature is divergent at one of its boundary points and moreover the upper limit of the curvature at that point is maximal possible, equal to 2, whereas the lower limit is -∞.

An extension of typically-real functions and associated orthogonal polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2011)

Annales UMCS, Mathematica

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 of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties...

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