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Geometric and Approximation Properties of Generalized Singular Integrals in the Unit Disk

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Abstract

The aim of this paper is to obtain several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness. In addition, these generalized integrals preserve some sufficient conditions for starlikeness and univalence of analytic functions. Also approximation results for vector-valued functions defined on the unit disk are given.

참고문헌 (8)

  1. "it Convergence ofgeneralized singular integrals to the unit", pp.511~ (2000), univariate case}
  2. "it Geometric and approximation properties of some singularintegrals in the unit disk"
  3. "it Convolution-type integral operators in complex approximation", pp.417~ (2001), \it Convolution-type integral operators incomplex approximation}
  4. "it On Beatson convolution operators in the unit disk", pp.101~ (2002)
  5. "it Geometric and approximate propertiesof convolution polynomials in the unit disk" (2005), in press.
  6. "it Degree of approximation of continuous functionsby some singular integrals", anal. num\'er. th\'eor. approx., pp.251~ (1998)
  7. "it Geometric theory of univalent functions", pp.8~ (1999)
  8. "\it Complex analysis" (2002), Cambridge University Press

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