On Convex Functions with Complex Order Through Bounded Boundary Rotation


Aydoğan S. M., Sakar F. M.

Mathematics in Computer Science, cilt.13, sa.3, ss.433-439, 2019 (Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s11786-019-00405-8
  • Dergi Adı: Mathematics in Computer Science
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.433-439
  • Anahtar Kelimeler: Analytic function, Convex function, Radius of starlikeness, Coefficient estimates
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

Let F be the class of functions f(z)=z+a2z2+&#x22EF;" role="presentation" >f(z)=z+a2z2+ which are analytic in D={z:|z|&lt;1}" role="presentation" >D={z:|z|<1} and satisfies the condition

1+1bzf&#x2033;(z)f&#x2032;(z)=pt(z),(b&#x2260;0,b&#x2208;C,z&#x2208;D)" role="presentation" >1+1bzf(z)f(z)=pt(z),(b0,bC,zD)

where pt(z)=(t4+12)p1(z)&#x2212;(t4&#x2212;12)p2(z)" role="presentation" >pt(z)=(t4+12)p1(z)(t412)p2(z)t&#x2265;2,p1(z),p2(z)&#x2208;P" role="presentation" >t2,p1(z),p2(z)PP" role="presentation" >P is the class of analytic functions with the positive real part (Caratheodory class) then this function will be called convex function by means of bounded boundary rotation and denoted by K(tb). In this present paper, we will introduce this class and its some properties.