Abstract
In the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete–Szegö problem of this subclass is also acquired. Further, some special cases of our results are designated.
Highlights
Let A represent the class of all functions which are analytic and given by the following form ∞ s(z) = z + ∑ an zn (1)n =2 in the open unit disc E = {z : z ∈ C, |z| < 1}
For the functions s and r in E analytic, it is known that the function s is subordinate to r in E given by s(z) ≺ r (z), (z ∈ E), if there is an analytic Schwarz function w(z) given in E with the conditions w (0) = 0 and
It is obvious that every univalent function s has an inverse s−1, introduced by s(s−1 (z)) = z (z ∈ E), Mathematics 2020, 8, 1888; doi:10.3390/math8111888
Summary
Let A represent the class of all functions which are analytic and given by the following form s(z) = z + Let S be class of all functions belonging to A which are univalent and hold the conditions of normalized s(0) = s0 (0) − 1 = 0 in E. It is obvious that every univalent function s has an inverse s−1 , introduced by s(s−1 (z)) = z (z ∈ E), Mathematics 2020, 8, 1888; doi:10.3390/math8111888 The class of all functions s ∈ A, such that s and s−1 ∈ A are both univalent in E, will be denoted by σ.
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