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- Title
CERTAIN RESULTS OF STARLIKE AND CONVEX FUNCTIONS IN SOME CONDITIONS.
- Authors
YILDIZ, Ismet; SAHIN, Hasan
- Abstract
The theory of geometric functions was first introduced by Bernard Riemann in 1851. In 1916, with the concept of normalized function revealed by Bieberbach, univalent function concept has found application area. Assume f(z)=z+Σn>2(anzn converges for all complex numbers z with 1,|z|, and f(z)is one-to-one on the set of such z. Convex and starlike functions f(z) and g(z) are discussed with the help of subordination. The f(z) and g(z) are analytic in unit disc and f(0)0,f'(0)=1, and g(0)=0,g'(0)-1=0. A single valued function f(z) is said to be univalent (or schlict or one-to-one) in domain DCC never gets the same value twice; that is, if f(x1)-fz2 for all z1 and z2 with z1= z2. Let A be the class of analytic functions in the unit disk U={z:|z|1} that are normalized with f(0)=0,f'(0)=1. In this paper we give the some necessary conditions for f(z)E S*[a,a²] and 0< a²<a<1 ... This condition means that convexity and starlikeness of the function f of order 2-r.
- Subjects
STAR-like functions; CONVEX functions; UNIVALENT functions; GEOMETRIC function theory; ANALYTIC functions; COMPLEX numbers
- Publication
Thermal Science, 2022, Vol 26, pS719
- ISSN
0354-9836
- Publication type
Article
- DOI
10.2298/TSCI22S2719Y