Coefficients Estimates of Bi-Univalent Functions Defined by New Subclass Function

Abstract

In this paper, we introduce and investigate some new subclasses S γ n , q ( λ , m , ϕ ) and W x k , α ( λ , δ , ϕ ) of bi-univalent functions in the unit disk U, which satisfies the qusi-subordination condition. We obtain estimates the first two Taylor-Maclarurin coefficients |a 2| and |a 3|.

On Some Sandwich Results of Univalent Functions Related by Differential Operator

“…Using the results (see [11,[18][19][20][21][22][23][24][25][26][27][28][29][30][31]) t𝑜 o𝑏𝑡ain suffici𝑒nt co𝑛𝑑itions for normalized an𝑎lytic functi𝑜ns to s𝑎𝑡isfy:…”

“…Als𝑜, Al-Ameedee et al [18,19] and El-Ashwah and Aouf [3] derived s𝑜me diff𝑒𝑟𝑒ntial sub𝑜𝑟𝑑ination an𝑑 sup𝑒𝑟𝑜rdination r𝑒𝑠ults f𝑜r analytic f𝑢nctions in 𝕌. Recently, several researchers obtained sandwich theorems for subclasses of analytic functions (see [3,[5][6][7][8]10,[12][13][14]18,20,[26][27][28][29][30][31]) . In [32], Catas ext𝑒nded the multi𝑝𝑙ier transfor𝑚ation and def𝑖𝑛𝑒d the o𝑝𝑒rator 𝑆 𝛼,𝛽,𝜆,𝛿 𝑘 on B, which is defined a𝑠 f𝑜llows:…”

Some Applications of Quasi-Subordination for Bi-Univalent Functions Using Jackson’s Convolution Operator

“…Several authors studied quasi-subordination of bi-univalent for another conditions, like, [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Throughout this idea, it is assumed ( ) is analytic and univalent with positive real part in and let ( ) ( ) ( ) Also, let ( ) be an analytic function in and…”

Revised Manuscript On New Sandwich Results of Univalent Functions Defined by a Linear Operator

“…The well-known monograph of Mocanu and Miller [5] and the supplemental recent book of Bulboacă [1,9] gave more details to the theory of differential subordination, subordination and superordination, with showing a definition of the Srivastara-Attiya transformation. The recent results are also given by several on Differential subordination, such as ( [10][11][12][13][14][15][16][17][18][19][20]). So that we have to generalize the function of Hurwitz-Lerch that is defined in [21] with following sequence:…”