On Sandwich Theorems Results for Certain Univalent Functions Defined by Generalized Operators

Abstract

In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.

On Some Sandwich Results of Univalent Functions Related by Differential Operator

“…They also considered the problem of determining con𝑑itions and ad𝑚𝑖ssible fu𝑛𝑐tions Ψ such that (1.5) is satisfied which implies p(𝑧) ≺ 𝑞(𝑧), for all functions 𝑝(z) ∈ ℳ. Moreover, they found con𝑑𝑖tions so that q is the sm𝑎𝑙lest fun𝑐𝑡ion witℎ thi𝑠 pro𝑝erty which is called the 𝑏est d𝑜𝑚inant of the su𝑏𝑜rdination (1.5).See also [1,3,[5][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…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:…”

Negative Coefficients Subclass of Multivalent Functions

“…Definition 1 [6], [7] : Let and be analytic which are in the unit disk . Then we say that is subordinate to , denoted by or ( ) ( ) if there exists a Schwarz function with ( ) , │ ( )│˂ 1 ( ) which is analytic in , such that ( ) = ( ( )) (…”

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…”