Application of the Subordination Principle to the Harmonic Mappings Convex in One Direction with Shear Construction Method

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

JOURNAL OF INEQUALITIES AND APPLICATIONS, cilt.2010, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2010
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1155/2010/896087
  • Dergi Adı: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

Any harmonic function in the open unit disc D = {z vertical bar vertical bar z vertical bar < 1} can be written as a sum of an analytic and antianalytic functions f = h(z) + <(g(z))over bar>, where h(z) and g(z) are analytic functions in D and are called the analytic part and the coanalytic part of f, respectively. Many important questions in the study of the classes of functions are related to bounds on the modulus of functions (growth) or the modulus of the derivative (distortion). In this paper, we consider both of these questions.