Some Differential Subordination and Superordination Results of p-valent Functions Defined by Differential Operator

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:…”

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…”

Some Results of New Subclasses for Bi-Univalent Functions Using Quasi-Subordination

“…Ma and Minda [14], using the method of subordination of defined and studied classes S * (Φ) and G * (Φ) of starlike functions. See also [15,16]…”