2019/01/09 by Hesam Mahzoon, Mahzoon, Hesam, Rahim Kargar +1
Materials Science · Mathematics · #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Polymer Synthesis and Characterization
paper · pdf · doi:10.48550/arxiv.1901.02670
openalex publication_date 2019/01/09 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
Let \A be the family of analytic and normalized functions in the\nopen unit disc |z|<1. In this article we consider the following classes\n n
mathcalR(
alpha,
beta):=
left
f
in
mathcalA:
rm\nRe
left
f'(z)+
frac1+ei
alpha2zf''(z)
right
gt;
beta,
, |z|lt;1
right
\n and n
mathcalL_
alpha(b):=
left
f
in
mathcalA:
left|f'(z)\n +
frac1+ei
alpha2zf''(z)-b
right|lt; b,
, |z|lt;1
right
,\n where -\π<\α\≤ \π, 0\≤ \β<1 and b>1/2. We\nshow that if f\∈ \R(\α,\β), then rm Re f'(z) and\n rm Re f(z)/z are greater than \β, and if\nf\∈\L_\α(b), then 0< rm Re f'(z) <2b. Also, some another\ninteresting properties of the class \L_\α(b) are investigated.\nFinally, the radius of univalence of 2-th section sum of f\∈\n\R(\α,\β) is obtained.\n