Distortion estimate and radius of starlikeness for generalized p-valent close-to-star functions

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Özkan H. E., Yavuz Duman E., Polatog̃lu Y.

International Journal of Mathematical Analysis, cilt.7, sa.17-20, ss.957-964, 2013 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 17-20
  • Basım Tarihi: 2013
  • Doi Numarası: 10.12988/ijma.2013.13093
  • Dergi Adı: International Journal of Mathematical Analysis
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.957-964
  • Anahtar Kelimeler: Close-to-star function, Distortion estimate, The radius of starlikeness
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

Let A(p, n), n ≥ 1, p ≥ 1 be the class of all analytic functions in the open unit disc D = {z| |z| < 1} of the form f(z) = zp + anp+1znp+1 + anp+2znp+2 + · · ·. Let g(z) be an element of A(p, n) such that g(z) satisfies the condition Re (z g'(z) / g(z)) > 0 for all z ∈ D, we then call g(z) the generalized p-valent starlike function in D. The class of such functions is denoted by S*(p, n). Let s(z) be an element of A(p, n) and g(z) be an element of S*(p, n). If the condition Re (s(z) g(z)) > 0 (z ∈ D), is satisfied then s(z) is called the generalized p-valent close-to-star function in D. The class of such functions is denoted by S*K(p, n). The aim of this paper is to give a distortion estimation and the radius of starlikeness of the class S*K(p, n).