New Results on Higher-Order Differential Subordination and Superordination for Univalent Analytic Functions Using a New Operator

Abstract

We present several new results for higher-order (fourth-order) differential subordination and superordination in this paper by using the new operator Hα,β,𝛿,𝜉,γ,nf(v) and offer numerous new findings for fourth-order differential subordination and superordination The innovative discoveries presented here are connected to those mentioned in previous articles. The differential subordination theory’s characteristics and outcomes are symmetric to the properties gained. Sandwich-type theorems are created by merging differential superordination theory with sandwich-type theorems.

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].…”

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…”

Analysis of Mixing Efficiency in a Stirred Reactor Using Computational Fluid Dynamics

“…Rahimi, Lassin, and others studied hollow impeller effects to validate experimental fluid dynamics using CFD in order to evaluate the influence of the impeller speed [28][29][30]. Some authors simulated lead bullion in hemispherical vessels known as kettles [9][10][11][12]14,15,[31][32][33][34]. Other authors have studied fluid flow dynamics in reactors for different purposes, such as the analysis of resin beads and ways of scaling up.…”

“…Murthy, Zhong Zhang, Sossa-Echeverria, Szalai, and others have dedicated their works to evidencing the influence of tanks and impeller geometries [16][17][18][19][20][21][22][23]35,36]. Some of them have used the residence time distribution method to analyze efficiency in a stirred tank [12,15,[26][27][28][29][30][31][32][33][34][41][42][43]. Others have simulated dissolutions in tanks and validated these procedures as appropriate for establishing physical parameters to improve mixing [11,12,[16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”