Bi-univalent functions of complex order defined by Hohlov operator associated with legendrae polynomial

Abstract

<abstract><p>In this paper, we introduce and investigate two new subclasses of the function class $ \Sigma $ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $ |a_2| $ and $ |a_3| $ for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.</p></abstract>

A New Pseudo-Type κ-Fold Symmetric Bi-Univalent Function Class

“…In addition, we have uncovered pertinent links to previous results and given a few observations. This paper could inspire researchers towards further investigations using the (i) integro-differential operator [31], (ii) q-differential operator [32], (iii) q-integral operator [33], and (iv) Hohlov operator [34].…”

On τ-Pseudo-ν-Convex κ-Fold Symmetric Bi-Univalent Function Family

“…The problem to determine bound on |d κk+1 |, (k ∈ N − {1.2}) for the classes that have been examined in this paper remain open. Since the only investigation on the defined family was related to coefficient bounds, it could inspire many researchers for further investigations related to different other aspects associated with (i) q-derivative operator [35], (ii) integrodifferential operator [36], (iii) Hohlov operator linked with legendary polynomials [37] and so on.…”

Second Hankel Determinant for a New Subclass of Bi-Univalent Functions Related to the Hohlov Operator

“…In [3], Brannan and Taha obtained the non-sharp estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 | of S * Σ (α) and C Σ (α). Recently, many scholars have defined various subclasses of bi-univalent functions (see [4][5][6][7][8][9][10][11][12]) and investigated the non-sharp estimates of the first two coefficients of the Taylor-Maclaurin series expansion.…”