On coefficient estimates for a certain class of starlike functions

Abstract

We define the classes of strongly almost ω1-p ω+n -projective abelian pgroups and nicely almost ω1-p ω+n -projective abelian p-groups as well as we study their crucial properties. Our results support those obtained by us in

Applications of first order differential subordination for functions with positive real part

“…In 1992, Ma and Minda [10] considered a weaker assumption that h is a function with positive real part whose range is symmetric with respect to real axis and starlike with respect to h(0) = 1 with h ′ (0) > 0 and proved distortion, growth, and covering theorems. The class S * (h) generalizes many subclasses of A, for example, [11], S * sin := S * (ϕ sin (z)) [7], S * C := S * (ϕ C (z)) [21], S * R := S * (ϕ 0 (z)) [8], and S * := S * (ϕ (z)) [17,18]. Several sufficient conditions for functions to belong to the above defined classes can be obtained as an application of the following subordination results involving the lemniscate of Bernoulli and other well known starlike functions with positive real part.…”

On a subclass of analytic functions involving harmonic means

“…The class σ, called the class of bi-univalent functions, was introduced by Levin [7] who showed that |a 2 | < 1.51. Branan and Clunie [3] conjectured that |a 2 | ≤ √ 2. On the other hand, Netanyahu [10] showed that max f ∈σ |a 2 | = 4 3 .…”

Third Hankel Determinant for A Class of Functions with Respect to Symmetric Points Associated with Exponential Function

“…The maximum value of H 2 (2)has been investigated by several authors. For instance the reader can see the work initiated by Hayman [13], Noonan and Thomas [29], Janteng et al ( [14], [15]), Bansal [5], Lee et al [20], Liu et al [23], Raina et al [38], Ohran et al [31], Laxmi and Sharma [18], Rǎducanu and Zaprawa [37].Very recently, Zaprawa [47]…”